EDIT: Looked into this a bit more. Apparently ForbiddenWebsite has a weird glitch where, if two party members in a 4 man are the same Job (e.g. two BLMs) in a 3DPS party it will...randomly substitute one with a random Healer Job. If there's a rhyme or reason to it, I haven't see it. Regardless, the top compositions for speed runs do appear to be T/3D parties, with the traditional T/H/D/D party being approximately 13.5-22.5% slower, depending on dungeon. This doesn't change much since the deviation is relatively small (usually less than 2 minutes; for 5 Extreme runs in a week, this would save a total of around 10 minutes per week) and the speed running community for 4 mans is also very niche (meaning not a thing that the community as a whole cares about nor that the Devs balance around). Moreover, these are the top/best speed run results in the entire data set, not an average/what most players would experience attempting the same thing. But putting it here for the sake of completeness/awareness. Whether the difference is noticeable or worthwhile to you probably depends on what your reliable dungeon running group consists of and how much effort or coordination you do or don't wish to use. :ENDEDIT
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While pre-made speed runs don't matter to the majority of the community and very likely don't matter to the Devs, the claim is often made that the Tank/3DPS party is outright superior for clearing 4 man content at the fastest rate. So, what do the numbers say?
Overall: (done by rating, not by time, though I think it's a proxy for time)
#1 is WAR/NIN/SAM/DNC - 710.74
#2 is WAR/SCH/BLM/SAM - 701.38 (a difference of -1.3169...% from #1, so less than 1.5% difference)
Dead Ends:
#1 is PLD/SCH/BRD/BLM - 10:48
#2 is PLD/SCH/BLM/DRG - 11:09
#3 is GNB/AST/NIN/BLM - 11:12
#4 is first no-healer party WAR/MCH/DRG/BLM - 11:27 (39 sec longer than #1)
Smiletown:
#1 is GNB/AST/NIN/BLM - 8:32
#2 is WAR/MCH/DRG/BLM - 9:22 (50 sec longer)
Stigma Dreamscape:
#1 is WAR/MCH/DRG/BLM - 9:07
#2 is WAR/WHM/NIN/BLM - 9:11 (4 sec slower)
Alzadaal's Legacy:
#1 is WAR/MNK/DRG/BLM - 9:13
#2 is GNB/AST/NIN/BLM - 9:17 (4 sec slower)
Fell Court of Troia:
#1 is GNB/AST/NIN/BLM - 9:30
#2 is WAR/WHM/NIN/BLM - 9:38
#3 is PLD/BLM/RPR/DNC - 10:57 (87 sec or 1 min 27 sec slower)
Lapis Manalis:
#1 is PLD/BLM/RPR/DNC - 10:55
#2 is WAR/WHM/NIN/BLM - 10:57 (3 sec slower)
In many cases, the standard party is the fastest clear of these 4 mans. In the cases it ISN'T, the Tank/3DPS clears are literally only a few seconds (3 or 4) faster.
This indicates that, in a coordinated party speedrunning content AND reporting on it (the forbidden website), there seems to be no real advantage to running T/3DPS over the standard T/H/D/D comp. And in several cases, the T/3D comp is actually slower. In one case by more than a minute.
Moreover, looking at Lapis Manalis specifically (since we can't "overgear" the content yet like we can the lower ones), the difference between the #1 and #50 party is 10:55 (655 sec) vs 12:01 (721 sec), a difference of 1 minute and 6 seconds. So we're not exactly talking massive differences here.
While it is absolutely true that a lot of the fast times ARE the T/3D comps, the fact remains that they are not the FASTEST in all cases, and where they are, are only so by a smidge. This means, when well played by a coordinated group, the time gap is relatively insignificant. And in some cases, the fastest clears ARE with the standard T/H/D/D, meaning for some dungeons, T/H/D/D is faster than T/3D.