In short...ban Drizzle, keep Drought, or keep both. I personally believe both weathers are viable for UU as UU is a more hostile environment than the now mainly stable OU and UU allows for experiemntation, for starters...but here are some points I want to address if weather were banned.
First: Houndoom cannot have its mega stone if better mega options exist in OU so if you want mega houndoom, you have to give up on Zard Y. Arguably better drought users are out there, ones that can hold heat rock...but Zard Y packs a menacing 417 attack without modest nature and keeps its sp. attack at said level when not in sun, also having a ground immunity and bulky enough to tank a couple water attacks, viably run roost in sun. While boasting an incredible sp. attack stat, Mega houndoom is a frail glass cannon, and cannot stand up to multiple U-turns going around. Scarf lando eats it for breakfast. At best I might imagine Mega houndoom pulling a late game sweep once all mons 362 speed and faster are dead, but that almost never happens. Chansey tanks hits for days, heatran destroys you, forcing you to pull HP ground if you want to sack a move slot for it, and almost any bulky mon can eat a hit to t-wave you. Houndoom cannot survive in OU and becomes worthless.
Second: Rain is an extremely viable option in OU as you have pelipper followed immediately by switching into Pert, or slow U-turn into pert, where as no drought user gains U-turn as a knowledgable move and becomes mind games when you switch into your specific mon. On top of this, a side note...fun fact, if you will...the only Chlorophyll mon in OU is Tangrowth...for christ sakes.
Third: Following the heels of the last point...all Chlorophyll users are frail in general, and all who naturally get chlorophyll are doubling their speed at the cost of getting absolutely murdered by opposing fire type attacks in the sun. The bulkiest options, Tangrowth, Venusaur and Tropius are obliterated by fire type attacks in response. Risk vs reward, right? Wrong. Rain doesn't have to deal with this...PERIOD!!! You have to deal with 100% accurate thunders and hurricanes, but rain beats sun clean through the gate. Kingdra, which usually runs Z or specs, absolutely no bulk required? Well according to the damage calc:
+6 252+ SpA Houndoom-Mega Fire Blast vs. 4 HP / 0 SpD Kingdra in Rain: 108-127 (36.9 - 43.4%) -- guaranteed 3HKO
I'm not even joking, the Kingdra in this situation has literally the same EV spread as the "OU specs" option, having 4 HP EVs on complete random...and Mega houndoom, the biggest culprit going throughout this whole forum, cannot touch it. "Oh well, just predict the switch or just use dark pulse"
Okay...
+6 252+ SpA Houndoom-Mega Dark Pulse vs. 248 HP / 252+ SpD Klefki: 237-280 (74.7 - 88.3%) -- guaranteed 2HKO after Leftovers recovery
+6 252+ SpA Houndoom-Mega Dark Pulse vs. 252 HP / 252 SpD Blissey: 388-457 (54.3 - 64%) -- guaranteed 2HKO after Leftovers recovery
+6 252+ SpA Houndoom-Mega Fire Blast vs. 252 HP / 252 SpD Blissey in Rain: 265-313 (37.1 - 43.8%) -- 99.8% chance to 3HKO after Leftovers recovery
+6 252+ SpA Houndoom-Mega Fire Blast vs. 248 HP / 192+ SpD Assault Vest Muk-Alola in Rain: 210-247 (50.8 - 59.8%) -- guaranteed 2HKO
+6 252+ SpA Houndoom-Mega Dark Pulse vs. 248 HP / 192+ SpD Assault Vest Muk-Alola: 153-180 (37 - 43.5%) -- guaranteed 3HKO
And that's if you even get up to +6 in the first place. The odds you get that far without a swift swim mon taking you out first is closer to zero, and getting one nasty plot up, if at all, is hard to do on its own in UU. OU has even bigger threats!!!
+6 252+ SpA Houndoom-Mega Dark Pulse vs. 248 HP / 252+ SpD Eviolite Chansey: 282-333 (40.1 - 47.3%) -- guaranteed 3HKO
+6 252+ SpA Houndoom-Mega Fire Blast vs. 248 HP / 252+ SpD Eviolite Chansey in Rain: 193-228 (27.4 - 32.4%) -- guaranteed 4HKO
+6 252+ SpA Houndoom-Mega Dark Pulse vs. 252 HP / 4 SpD Unaware Clefable: 82-97 (20.8 - 24.6%) -- possible 6HKO after Leftovers recovery
+6 252+ SpA Houndoom-Mega Fire Blast vs. 252 HP / 4 SpD Unaware Clefable in Rain: 112-133 (28.4 - 33.7%) -- 97.7% chance to 4HKO after Leftovers recovery
Heatran may die to a +6 Dark pulse but is completely immune to flamethrower and sludge bomb variants, and absolutely eats solar beam for days, even non bulky variants could take hundreds.
Fourth: Drizzle in UU is already broken as it is. You have two top contenders already in Kingdra and Ludicolo who abuse their weather, gain an additional fire downgrade and monstrously boost their own water stabs...but you also have the non water types? Mega manectric thunder, Moltres Hurricane, Swift swim or Water absorb Seismitoad, Muk as stated above can abuse the rain to either absorb strong hits from Mega houndoom, Venusaur, Lilligant and be a bulky pivot by scaring them off or hard doubling to a swift swim mon. All drought users are specially based (or prioritize it) and get eaten by Alolan muk who can pursuit trap or knock off heat rock.
Fifth: Non speed nature variants of Venusaur and Shiftry and all options slower than those cap out at 518 speed maximum, where as scarf Infernape with speed nature (granted this is one scenario), outspeeds by one point at 519. So not even accounting for all the other things I have to worry about, now I have to give up damage potential for speed just to make sure I don't get taken out by a flare blitz monkey. "Oh well, just switch into Houndoom" Okay well one, if this guy is smart he would know to do that and close combat/focus blast... Or if I mega evolved previously...
252 Atk Infernape Flare Blitz vs. 0 HP / 0 Def Houndoom-Mega: 92-108 (31.6 - 37.1%) -- 84.6% chance to 3HKO
So I'm resisting this attack, he is not attack nature invested, and he's still chunking 1/3 of my life in a hit I couldn't avoid.
If he's special? Oh god:
252 SpA Infernape Fire Blast vs. 0 HP / 4 SpD Houndoom-Mega in Sun: 126-148 (43.2 - 50.8%) -- 98.4% chance to 2HKO after Solar Power damage
Houndoom is not a tank and was not designed to be one, so this argument is INVALID.
Sixth: On top of sun practically getting invalidated in OU by fellow weather...Hawlucha exists. Most run Acrobatics, most run SD or sub, but almost all can counter all chlorophyll users even without speed nature. Lucha cannot do the same to most rain mons like Pert and Kingdra, Ludicolo can live an HJK, and on the off chance said rain team is running Pex? Lucha is done. Sun cannot say the same thing. If Lucha were to set up unburden immediately, the only mon who might stand a chance is Max defence torkoal...but...
+2 252+ Atk Hawlucha High Jump Kick vs. 252 HP / 252+ Def Torkoal: 210-247 (61 - 71.8%) -- guaranteed 2HKO after Leftovers recovery
Let alone if torkoal survives that long to begin with, to live at full HP and tank the first hit so he can potentially burn Lucha in return. Lucha is actually the scariest option possible as, after unburden, not a single mon can outspeed. Most sun teams don't run an unaware mon on them and cannot take a hit anyways.
Seventh: By banning rain, which is the most natural counter to sun regardless, Sun doesn't just get a free run and it's unfair to consider these two weathers on par with one another. If anything, you're essentially banning one because they're similar to another, and that's not what should be done. Sun also has a potentially easy time against teams with no synnergy, and stall provided you setup, as UU doesn't have fearsome unaware clef and chansey. But on top of all of that, you also have weathers in the lower tiers coming to UU. Mega abomasnow, Vanilluxe, Aurorus, Hippowdon, Gigalith all have hail and sand stream respectively...plus you have insane options like cloud nine mons, Golduck, Lickilicky, Drampa, freaking Altaria before mega evolution? Why are people not even mentioning this!?! They exist too, and especially Abomasnow and Hippowdon get used a lot in UU so why are we just acting like we're only talking about sun and rain here?
Eighth: Banning sun means being forced to run it in OU. OU invalidates sun with two mons: Pelipper and Tyranitar. You could bring two drought users, more specifically Torkoal with heat rock, and either Ninetails with heat rock or Zard Y, but at the end of the day you have a very limited movepool of options to take into OU that are viable. You have a strong hitting Venusaur and Lilligant, and they somewhat threaten Pelipper or Tyranitar, but Heatran invalidates both options without HP ground. Run HP ground? You're now unable to touch Scizor before he obliterates you with U-turn. You are forced to bring a bare minimum of a rapid spinning torkoal or a defog option in Shiftry but Shiftry is nowhere near bulky enough to survive before defog can be used. Tornadus Therian can easily run rain dance if required but let alone, usually runs flyinium Z or rocky helmet. Helmet variants invalidate the use of physical chlorophyll mons unless we're talking tangrowth, but without a swords dance, Tangrowth cannot do half to Tornadus even with rock slide, adamant nature, and Torn can just take it out. Z options are close to nil but the top tier options are Venusaur/Victreebel poisonium, Moltres Flyinium/Firium, or considering you're now fearing sp. defensive heatran you might want to run Fightinium on Sawsbuck for all I know, but then you're fearing Landorus Therian cuz he'll just eat it up.
Do NOT ban Drought, please. This ability may seem powerful, but you're not considering the after effects and even the current environment we're in as of now. By banning sun to OU, you have too many threats that exist that eat up sun teams as it is, and better rain options are also in OU. UU is a harsh environment that doesn't easily allow in Sun to begin with and climbing the ladder with with it past the 1400's is harsh as it is. I can easily go and get more replays for you, but the summary is that I cannot consistently get past the 1400's with sun, merely the cusp of 1500 is the highest I have ever achieved with it even with good predictions on my side.
Ban Drizzle, the options vary too heavily and can easily work in OU as well as UU as they are. I've gone into the bullet points detailing where rain is superior and I believe it should be restricted to OU. By banning it, you are not just "giving" the meta over to UU as there are hundreds of options that counter sun to begin with, let alone sticky web lowering any and all chances of success if torkoal is dead and cannot rapid spin in time.
I will post more replays if asked. I still stand by the side of just banning rain, and do not wish for sun to be banned.