I bought The Last Word (300) ages ago when Xur sold it, but I never used it much, and it's sat in my vault. I thought I'd only ever use it in Crucible if I ever did use it, so I never upgraded it. I recently got 331 version of The Last Word from VoG, so I thought it was a good opportunity to level it up and compare the damage between the two, in order to put a number of myths to bed.
What I've done is recorded the precision damage against enemies at various levels. I've chosen to use thrall for the testing, because they are abundant at a number of levels, and are the easiest enemy to access at level 30+. I've found that the damage done to thrall, acolytes, dregs, and vandals is exactly the same as long as they are red bar enemies; however, for consistency I have chosen to test against thrall wherever possible.
I have chosen to record the damage at a number of different character levels, to also show how different levels affect the damage output.
It's difficult to present the data on the forum, so I'll post it in three columns. The first column is the level of the enemy, the 2nd column is the precision damage of The Last Word (300), and the 3rd column is the precision damage of The Last Word (331).
As a Level 28 character
03 - 406 - 406
06 - 497 - 497
09 - 609 - 609
12 - 746 - 746
15 - 913 - 913
18 - 1119 - 1119
20 - 1281 - 1281
22 - 1281 - 1466
24 - 1281 - 1466
26 - 1281 - 1466
28 - 1281 - 1466
30 - 705 - 807
31 - 615 - 704
33 - 0000- 0000
So what you can see here is that up to and including level 20, there is no difference in damage between either gun, regardless of one having a higher attack level than the other. We know at lower levels that there is a damage cap applied so that high powered guns aren't wiping out every enemy in one hit. We know that damage is based on a formula of a gun's attack rating combined with its impact, plus other modifiers (I don't know the formula). Since these guns are identical apart from the attack rating, it's logical to assume that for each enemy level, the game applies a hard cap to a gun's attack level to keep its damage down. You can see that the 300 gun maxes out damage at 1281, which happens first happens against level 20 enemies. Since the 331 gun is still only hitting 1281 damage on those enemies I think it's fair to assume that the hard cap on the attack rating at that level is 300. Only once you start attacking level 22 enemies does that 331 gun's damage rise to its max of 1466. My hypothesis is that this trend will continue with the 360 level guns, in that they will not max out damage until level 24 enemies, but that cannot be tested at the moment.
You'll notice a drop in damage at level 30 and level 31. This is due to facing enemies higher than my own current level of 28, so the game applies an arbitrary damage penalty of 45% less damage for being two levels below, and 52% less damage for being three levels below the enemy. There is absolutely no damage done to enemies four levels above our own level.
You will noticed that the change in damage between levels 3-20 is rather linear, with each jump up of three levels being around 18%, and the jump of two levels being about 12% (so roughly 6% increase in damage cap per level).
You'll also notice that the difference in damage between either gun once you are facing level 22 enemies and above is also entirely uniform at approximately 12.6% at every level. It does not change at all.
As a Level 29 character
03 - 406 - 406
06 - 497 - 497
09 - 609 - 609
12 - 746 - 746
15 - 913 - 913
18 - 1119 - 1119
20 - 1281 - 1281
22 - 1281 - 1466
24 - 1281 - 1466
26 - 1281 - 1466
28 - 1281 - 1466
30 - 871 - 997
31 - 705 - 807
33 - 0000- 0000
As we go up a level, things are more or less the same. Up to level 28 there is absolutely no change. The only differences now are the drops in damage at level 30 and 31, where we get the arbitrary damage penalty again. The penalty for being one level below is 32% less damage, and for two levels below, it's 45% less damage, as before. Again, the different in damage between the two guns is uniform at 12.6%.
As a Level 30 character
28 - 1281 - 1466
30 - 1281 - 1466
31 - 871 - 997
33 - 615 - 704
This time I've just omitted all the lower level damage to save space, as you can see from the last set of data, it's exactly the same. You can now see we are at a high enough level to damage level 33 enemies. Once again, the results are consistent. The only changes in damage are due to the reduction in damage caused by being a lower level than the enemies faced, and again it's the predictable 32% and 52% deductions. There is no extra damage being done by the 331 gun against a level 33 enemy, and the difference in damage between the two guns is that uniform 12.6% at all levels.
As a Level 31 character
28 - 1281 - 1466
30 - 1281 - 1466
31 - 1281 - 1466
33 - 705 - 807
Really predictable now. The only deduction against level 33 is for being two levels below - 45%.
As a Level 32 character
28 - 1281 - 1466
30 - 1281 - 1466
31 - 1281 - 1466
33 - 871 - 997
Would not have expected anything different. The only deduction against level 33 is for being one level below - 32%.
Okay, so a final set of data I have is just from running a level 32 char with a variety of guns against different level enemies. Again, I'll have to do it in columns because it's difficult to display, but there's some decent results. First column is the level of enemy, 2nd column, is damage for Word of Crota (331), 3rd column is damage for Thorn (331), 4th column is damage for Fatebringer (300), 5th column is damage for Regulator Mk. 56 (146), 6th column is for Regulator Mk. 56 (244).
03 - 426 - 469 - 477 - 527 - 527
06 - 522 - 574 - 584 - 646 - 646
09 - 639 - 703 - 715 - 671 - 791
12 - 783 - 861 - 876 - 671 - 909
15 - 959 - 1055 - 1073 - 671 - 1187
18 - 1175 - 1292 - 1315 - 671 - 1187
20 - 1281 - 1479 - 1505 - 671 - 1232
22 - 1540 - 1694 - 1505 - 671 - 1232
24 - 1540 - 1694 - 1505 - 671 - 1232
26 - 1540 - 1694 - 1505 - 671 - 1232
28 - 1540 - 1694 - 1505 - 671 - 1232
30 - 1540 - 1694 - 1505 - 671 - 1232
31 - 1540 - 1694 - 1505 - 671 - 1232
33 - 1047 - 1152 - 1024 - 456 - 838
Notice that the 331 guns all have increased damage against level 22, whereas the 300 guns do not (as before).
Notice that the (rare) Regulator hand cannons are actually harder hitting than the legendary weapons until their damage maxes out, due to them being higher impact, further strengthening the theory that it's the guns attack rating that's capped based on enemy level.
Also notice that the only time any of these weapons drop in damage is when facing enemy above our character level, and it's the standard 32% drop in damage across the board for being one level below the level 33 thrall.
Conclusions:
At higher levels, a 331 gun always does more damage than a 300 version of the same gun. This notion that they only do more damage in a level 33 raid is nonsense.
There is an idea that a gun's attack rating divided by ten is the maximum level it will do proper damage at. Again, nonsense. A gun will generally max out damage at levels well below this, but will continue to do the same damage at all levels above.
A gun's damage does not tail off at higher levels. The only thing causing a drop in damage is being at a lower level than the enemy you are facing. THIS DAMAGE REDUCTION IS APPLIED EQUALLY TO ALL WEAPONS, it is not weapon specific. This happens at all levels, not just against level 33 enemies.
That's all I've got. Feel free to ask any questions. I hope this clears things up a bit. If anyone has any better ideas on how to display this data, I'm all ears. I have it all on a spreadsheet.
edit: typos taken care of
https://docs.google.com/spreadsheets/d/1mMX6wusOx9OG7ozAUXrIjpbLVoYunJ9chHrhCBK0RjU/edit?usp=sharing
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I find it impressive that we have video game community research projects. That was a large ass paragraph, but had a ton of info. Bump for you