Priority has proven to be very useful in Little Cup over the generations and, as such, it has gotten to be an extremely common tool used on just about every team. The levels of significance on how each priority move impacts the metagame is somewhat dependent upon the Pokemon who uses it. The top seven priority attacks from my perspective are as follows:
1. Life Orb Sneasel's Ice Shard is by far the strongest and most dominating priority attack in the tier right now. Its ability to revenge kill pretty much anything that switches into Knock Off/Ice Punch one or two times, even if they have priority, is outstanding. Sneasel has been banned.
2. Life Orb Carvanha's Aqua Jet is a close second, hitting many things in the tier incredibly hard off its 90 base Attack and STAB, with every turn of Speed Boost aiding it in outspeeding other priority users. Being notably strong in addition to having priority gives Carvanha a huge edge in many situations.
3. Choice Band Bunnelby's Quick Attack is one that some of you might not have expected to make it so high on this list. Its Huge Power ability lets it basically hit 26 Attack (most LC mons are lucky if they hit 18 or 19, let's be honest) without even running an Attack boosting nature. This, combined with Choice Band and STAB, knocks out almost any Pokemon from at least half health if it scores a neutral hit, and even OHKOs Murkrow easily after Stealth Rock damage. It might sound awkward that it has a Choice Band, but it also gets U-turn to duck out on the switch-ins who might try to block it while dealing a considerable chunk of damage before going to a check; please don't underestimate how potent this is. It can revenge-kill a ton of threats at a range that other priority attackers wouldn't be able to kill from, and it won't be easy to outplay.
4. Meditite's combination of Fake Out and Bullet Punch, when used in succession, can take down the monstrous Unburden Swirlix without letting it move and without activating its Berry Juice, thereby voiding Unburden's activation as well and knocking Swirlix out easily. Meditite's Pure Power ability adds that extra strength that it misses out on due to lack of STAB, and is a force to be reckoned with.
5. Tirtouga's Aqua Jet saves the day in many battles even without a Shell Smash. After a Shell Smash, however, it becomes a deadly revenge-killing option that can finish off foes who still have a fair bit of health left. Notable mons it can come in handy against include (but are not limited to) LO Sand Rush Drilbur and LO Sneasel (Ice Shard is resisted anyway).
6. Life Orb Murkrow's Sucker Punch was a huge contender last generation and it remains the case in XY Little Cup, being able to outspeed many other priority carriers and smack them brutally hard. It even outspeeds Sneasel's Ice Shard and Tirtouga's Aqua Jet after a Shell Smash if it runs a Scarf instead and it's actually powerful enough to finish off Sneasel after it has been weakened by prior damage, hazards, and/or its own Life Orb recoil, despite it being resisted.
7. Timburr's Mach Punch is still making its mark in this new generation (although the influx of Fairy-types somewhat hampers its usefulness) and it still can finish off faster foes after hitting hard and recovering with its Drain Punch. Although it's not as good this generation as it was last generation, it's not to be overlooked!
Apart from priority attacks, there are two very special abilities that give priority to multiple moves, and these deserve a very special mention here as well:
Gale Wings
This ability is exclusive to Fletchling in XY Little Cup and gives +1 priority to all Flying type moves. This not only means that Fletchling's powerful STAB Acrobatics (165 Base Power without an item) is able to outspeed its enemies and murder them at clutch moments in battle, but it also gives priority to Roost so that its health can be restored and its Flying type can be temporarily removed so that it doesn't take super-effective Rock, Ice, and Flying damage immediately afterward, which is pretty awesome. Gale Wings also gives priority to Tailwind, so that Fletchling can provide its teammates with doubled Speed right before biting the dust. This ability is a very powerful addition to the family of priority moves in Little Cup this generation!
Prankster
An ability carried over from last generation, Prankster gives every non-damaging move +1 priority, and the amount of buffs that can give to a few mons is actually quite incredible. Murkrow can use this ability to run its dreaded Parafusion (Swagger + Thunder Wave) set to annoying ends and also its tenacious SubRoost, all while having priority on all of these options before the foe can act. Cottonee can use this ability to Encore its enemies and lock them into setup moves or Stealth Rock, thereby rendering them useless and forcing them to switch out. Additionally, Cottonee can get priority on Stun Spore, Leech Seed, Taunt, and even Memento... so it can be pretty annoying and even scary under the right circumstances. One Pokemon that many players found particularly interesting last generation was Riolu, who makes use of the Prankster ability in tandem with the move Copycat, letting it basically have +1 priority on whatever move was used last in the battle, whether your own or your foe's. This allows Riolu to move twice against every switch-in, and even allows it to spam Roar to continuously shuffle the opponent's team through hazards. This ability was quite a strong addition last generation and it can be expected to shake things up in XY Little Cup as well!