Life Orb (at least in BW, I'm pretty sure they changed the trigger address at least for gen 6) has a modifier of 0x14CC and a trigger address of 21DEC65. Meanwhile Sheer Force has a modifier of 0x14CD and a trigger address of 21dbf48. Finally Analytic has a modifier of 0x14CD and a trigger address of 21dc6c0.
This means that they actually have what is normally a very slight damage variation, despite being "the same multiplier" boost. To illustrate this I went to the limits of absurdity in terms of damage - a level 100 Reshiram Blue Flare (good for our purposes due to being sheer force-able) vs a level 1 Paras.
252 SpA Life Orb Turboblaze Reshiram Blue Flare vs. 76 HP / 0- SpD Paras: 57774-67975 (481450 - 566458.3%) -- guaranteed OHKO
(57774, 58450, 59131, 59817, 60493, 61174, 61850, 62531, 63207, 63893, 64574, 65250, 65931, 66607, 67288, 67975)
252 SpA Sheer Force Reshiram Blue Flare vs. 76 HP / 0- SpD Dry Skin Paras: 72136-84868 (601133.3 - 707233.3%) -- guaranteed OHKO
(72136, 72984, 73836, 74680, 75532, 76380, 77224, 78076, 78924, 79776, 80620, 81472, 82320, 83172, 84016, 84868)
252 SpA Analytic Reshiram Blue Flare vs. 76 HP / 0- SpD Dry Skin Paras: 72136-84868 (601133.3 - 707233.3%) -- guaranteed OHKO
(72136, 72984, 73836, 74680, 75532, 76380, 77224, 78076, 78924, 79776, 80620, 81472, 82320, 83172, 84016, 84868)
[Analytic was properly applied by modifying base speed stats of Reshiram and Paras]
At this level of damage it's pretty clear that Sheer Force and Analytic are better than Life Orb, but this isn't always the case! Due to how the formula works you can get a very different result. (Since I hope I was convincing enough that for all intents and purposes Sheer Force and Analytic are identical, I'm only doing Sheer Force from now on.)
252 SpA Life Orb Reshiram Blue Flare vs. 0 HP / 0 SpD Abomasnow: 1409-1659 (438.9 - 516.8%) -- guaranteed OHKO
(1409, 1425, 1440, 1456, 1471, 1487, 1503, 1518, 1544, 1560, 1575, 1591, 1607, 1622, 1638, 1659)
252 SpA Sheer Force Reshiram Blue Flare vs. 0 HP / 0 SpD Abomasnow: 1404-1656 (437.3 - 515.8%) -- guaranteed OHKO
(1404, 1420, 1440, 1452, 1468, 1488, 1504, 1516, 1536, 1552, 1572, 1584, 1600, 1620, 1636, 1656)
Interestingly AnalyticForce is generally weaker than Life Orb at this point. This is the case even as you go further down - see:
252 SpA Life Orb Reshiram Blue Flare vs. 252 HP / 56+ SpD Eviolite Porygon2: 185-218 (49.4 - 58.2%) -- 98% chance to 2HKO
(185, 187, 188, 191, 192, 195, 196, 200, 203, 204, 207, 208, 211, 212, 214, 218)
252 SpA Sheer Force Reshiram Blue Flare vs. 252 HP / 56+ SpD Eviolite Porygon2: 184-217 (49.1 - 58%) -- 97.7% chance to 2HKO
(184, 186, 189, 190, 193, 195, 196, 199, 201, 204, 205, 208, 210, 213, 214, 217)
It's not much, and there are even some damage rolls where AnalyticForce is stronger on the same random [0.85-1.00] damage roll, shown in bold in the above calcs. This is even the case for a couple of the Abomasnow rolls (not shown in bold).
Funnily enough, this even goes down to LC to a noticeable enough extent. For example, Ponyta vs Porygon has Life Orb as the objective better modifier - not even a single roll is better with AnalyticForce
236+ SpA Life Orb Ponyta Blue Flare vs. 236 HP / 76+ SpD Eviolite Porygon: 13-17 (50 - 65.3%) -- guaranteed 2HKO
(13, 13, 13, 13, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17)
236+ SpA Sheer Force Ponyta Blue Flare vs. 236 HP / 76+ SpD Eviolite Porygon: 13-16 (50 - 61.5%) -- guaranteed 2HKO
(13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16)
In LC, luckily enough, we get to see similar behavior as Reshiram vs Paras without needing to go to the extreme of 5x weakness. A 2x will work fine.
236+ SpA Life Orb Ponyta Blue Flare vs. 0 HP / 0 SpD Snivy: 49-62 (233.3 - 295.2%) -- guaranteed OHKO
(49, 49, 49, 55, 55, 55, 55, 55, 55, 57, 57, 57, 57, 57, 57, 62)
236+ SpA Sheer Force Ponyta Blue Flare vs. 0 HP / 0 SpD Snivy: 50-62 (238 - 295.2%) -- guaranteed OHKO
(50, 54, 54, 54, 54, 54, 56, 56, 56, 56, 56, 60, 60, 60, 60, 62)
Here AnalyticForce has a lot of better rolls and a few worse ones. So overall?