As mentioned by a poster above, I prefer CT for its simplicity and ease of use. As was said, other versions add detail, but they also tend to clutter up the basic games mechanics in the process, interfering with the ease of use which made CT so easy to run and to play.
MegaTraveller lost me to Traveller because I didn't like the "galactic upheaval in known space" aspect which was suddenly made integral to the published setting. What I liked most about the Third Imperium was that it was an essentially stable backdrop which was still flexible enough to accomodate Referee preference. If you wanted a "space war and upheaval" campaign, you could certainly have that -- the Imperium was large enough that space wars could be furiously fought in certain quasi-autonomous regions, while other areas of the Imperium simply proceeded with life as normal.
Beyond the fact that I found the assassination of Strephon implausible as described in MT, I also found the idea that Strephon's murder alone would plunge the entire Imperium into war and disarray equally implausible. I just never saw the Third Imperium as being so fragile, with the weight and inertia of strong commerce and entrenched tradition behind it. The "reasons" given for the fall always felt like retroactive rationalizations to me.
TNE just didn't look or feel like Traveller to me. This, and the fact that they seemed to require you to buy umpteen supplements before you could run a full-option basic TNE game, put me off. Plus, that whole "out of the galactic night" setting gave adventures a spin I wasn't interested in. Again, I preferred the CT 3rd Imperium, where both the MT and TNE story-styles could be played out in sections of the existing setting. The Third Imperium was comprehensive and expansive enough as a setting to accomodate the themes and ideas presented in MT and TNE -- but MT and TNE were never large enough as settings to return the favour. Given a choice, I prefer an inclusive setting over an exclusive one.
I wanted to like T4, but the game wouldn't let me. Besides all the typos, omissions, and other technical problems, the game mechanics just didn't feel like Traveller to me. Add to this that there was again an emphasis on buying multiple books in order to run a full-featured basic game, and I just couldn't say yes to T4.
GURPS Traveller looks and feels like Classic Traveller to me in many respects (due in no small part, I'm sure, to Loren K. Wiseman being at the GT helm). The art and and layout on most of the GT stuff is beautiful, and just screams "Classic Traveller" to me. Heck, GT even ditched the whole Dead Strephon/Chaotic Imperium/Narrowed-Options Game Universe I'd found so hard to accept ...
But ... I just can't stand the GURPS system mechanics. If CT is elegant simplicity, then (to me, anyway) GURPS is inelegant complexity for its own sake. I'm not suggesting that the GURPS system is broken by any means, only that it's far more detailed and detail-oriented than either I or my players want or need.
Then we come to T20. It's what I'm using now. On the downside, the Character Generation rules are nowhere near as organized, clear, or self-explanatory as I would've hoped, and the artwork I've seen from QLI just doesn't measure up across the board, in my opinion. On the upside, it's d20-based, which makes it a LOT easier to entice current gamers to give my campaign a try. Also, the T20 setting is so similar to that of the CT Third Imperium that the differences are effectively negligible when I'm adapting scenarios and supplements to my own campaign. Lastly, the care and enthusiasm the T20 folks have for Traveller is obvious; I may not agree with them on their every interpretation of the Traveller universe, but that's not because they don't care, or don't try, or are more interested in pushing their specific version of the Traveller setting on me (a feeling I always got from MT and TNE) than they are in helping me to tell the Traveller stories I want to tell.
So, it's T20 for me for the forseeable future -- especially if we get better-caliber artwork, and a revised, re-edited, re-organized Traveller's Handbook somewhere down the line (although it seems like the upcoming T20 Player's Book is being designed to pick up the latter slack).
Of course, if the mythic T5 ever appears, and its rules are a return to the elegant simplicity of CT ...
Listlurker