I have a D54 that was built and tuned by Hector Medina. It is in .177 and has the T06 trigger.
It is set up to shoot JSB 8.44 pellets at 12 fpe and it shoots VERY well......if I do my part.
The trigger has a bit of a take up, maybe 1/4" or so, and then hits a wall. A continued press breaks the sear cleanly and as set up, there is no movement of the gun at all. I can see the pellets in flight the last 1/3'd of the way to the target. I have a custom stock made for it that has adjustable cheekpiece (comb), and is built for my length of pull. It is a thumbhole stock with vertical pistol grip, which I prefer, and I shoot with thumb up.
It is one of my favorite guns to shoot, only because I cannot pick a favorite between my other piston guns or my PCP's.
It is FUN to shoot!
Mark
here are the parts diagrams of the 3 trigger setups
http://www.omps2.it/en/firearm-spare-parts/diana-spare-parts/mod-54-54-t01.html
https://www.dropbox.com/s/toa880ku7kwqdnr/DIANA-54-AirkingT05.pdf
https://www.dropbox.com/s/jzuqr8rd1zqiepe/DIANA_54_Airking_T06.pdf
they are just show the make up of the trigger assemblies and nothing more
most say the TO6 trigger is the best but also that the TO1 can be made to be very nice
Trigger units: The T06 trigger unit is probably the best out of the box (i.e. new and unaltered) of the three, or at least the most-adjustable. And, unlike the other two you mentioned, it also has a metal trigger blade, and some people waited literally for decades for that metal trigger blade to finally arrive on air rifles made by Diana. If you hate a plastic trigger blade, that item alone may answer your question.
With those things being said, both the T01 and T05 can also be made to be very-nice and very-adjustable with a slight alteration to their trigger blades, a lube job, and possibly a slight stoning of the trigger sears. Now, you may have immediately noticed something in what I said there about the last two versions: unless you know how to tune the triggers yourself, the T06 may suit you best because it doesn't require your sending it off to an air gun tuner to do the mods I described on the other units. If you want to keep the rifle and trigger safe under your own roof, the T06 will probably suit you best.
Caliber: As far as caliber, some of that answer comes from what you want to use the rifle for. That was alluded to in the other post where the writer said he had his rifle set up for 12 FPE. The 54 is capable of much more power than that in either caliber, but if you have your heart set on that 'magic' 12 FPE, you may like the .177 caliber version better because .22 caliber at 12 FPE is fairly 'loopy' in its trajectory.
With those things said about caliber, I've found--as have the owners who sent me their 54 for a tune--that the rifle really shines in .22 caliber. It's a powerful hunter when set-up for standard factory power, and has enough velocity (plus the recoil-less operation) to yield high-accuracy even at further distances. To see what I mean, use one of the ballistic calculating apps on the Net and plug in '825 fps' muzzle velocity and '15 grains' in the blanks. That pellet will still be moving along pretty well at 50+ yards.
As a final item regarding caliber, I've seen MANY posts over the years where owners were wanting to convert their RWS 54 from .177 caliber to .22 caliber, but I can't remember even one instance where someone wanted to do the opposite. I'm not saying the issue has never been posted about, but it must be rare or I think I would have seen it by now.
Finally, I should tell you that I never owned an RWS 54 in either caliber, but I've tuned several in both calibers. I've fielded mail from their owners both before and after the tune. Except with the owners who wanted to use the rifle exclusively for Field Target (FT) shooting, everyone who had the rifle was glad they'd decided to get theirs in .22 caliber. And, I DID own an RWS 52, which I bought in .22 caliber, and I never came to second guess my decision and wish I'd bought it in .177 caliber. I only sold it because I was pressed for money at the time. It was a very-nice rifle.
It's worth a mention that the factory spring in the 54 has a tendency to some early breakage. It's not just the 54, though, The 34, and 48-52 have the same issue. Thus, it makes purchasing a good after-market spring a good investment (and fortunately it's a cheap upgrade). But, that breakage is equally-possible in both calibers, so it doesn't need considered as to caliber selection.
Oh, yeah, I almost forgot. The 54 puts a pretty-hard jolt on the scope during the shot cycle, partly-due to its anti-recoil-less action, so having one 'de-tuned' for less power may give you longer scope life. But, I'd still recommend you buy a good scope.
The T01 is quite a nice trigger as well is the T06. I would agree that the T06 is probably better out of the box. I believe Diana purposely held back the adjustability of the T01 by limiting the length of the adjustment screw, especially the the 1st stage screw. An easy fix is to file a flat under the screw giving it more adjustment range. This results in one nice trigger if it is then adjusted properly. And I agree with Ed here. Although it is not difficult, I would not advise doing this unless you are confident in your ability to do it properly.