To be honest, each of the settings has it's own appeal.
I'm talking SOLELY about setting issues, not rules.
TNE, as MAS states above, is a frontier "Wild West in Outer Space" kind of feel.
MT lends itself to a Space: Above and Beyond feel, as well as a Battlestar Galactica feel, while not preventing the "Smash and Grab". It actually lends itself well to a "Pirates are Everywhere" feel, too.
CT tends to be more of a Heinlein, Asimov, Drake, Cole-and-Bunch, and Brinn kind of feel - part of the larger whole, but still, peace isn't everywhere. But where there is peace, there is intrigue, politics, and merchantile endeavour.
T4 is more exploratory, and feels a little more Bujold, Webber, and Cole-and-Bunch. The universe isn't tamed, but the safes are... and politics, intrigue, and interpoility relations make a huge difference.
T20 is, setting wise, CT, with a bujold and cole-and-bunch influence. Individuals can make a difference, cause they're out on the edge of things, and the safes are a way off. Tension, cold war, and intrigue.
GT is a much more homogenous version of CT. PC's are even less relevant, because the simulationist nature of the line... so GT is one where tramps live off the scraps the lines can't handle, and many standard traveller trophes are altered, subtly and slightly. (I still don't see IM Cooks being in battle dress unless assigned to a foot unit. It's a different take on the CT model, with a much less space opera approach.
Traveller 2300 puts forth a wonderful setting, rife with war, politics, and business opportunity; humanocentric, but not the same universe as the other Traveller games. ( Came out just at the time that Traveller was coming to mean the setting, rather than the base assumptions of Science Fiction Adventure with Fairly simple but realistic rules.)
Traveller is a collection of variations on the theme, but each ruleset tried to support the trophes that the setting puts forward. Each can runn any of these trophes, but each ruleset supports certain things better.
CT has loads of support, and is the blanded ruleset. Marginally compatible mass combat (Striker) and boarding action (AHL), sector and world level combat systems (5Fw and Invasion Earth), and alternate versions of personal combat and ship combat (Bk1, Snapshot; Bk2, Mayday, HG). Small scale and large scale merchanting rules. Two ship design systems, and an unrelated vehicle design (Bk2, Bk5, Striker). Scads of support materials. Very limmited character growth in play. Psionics very potent, but limited useage. Almost no art.
MT: the combat system is integrated for all scales except ship-on-ship. CG is ballanced better between basic and advanced. Large Scale commerce rules only. Rules for turning the personal combat into unit combat, on levels from man/vehicle to Regiment/Wing. Research rules. More detailed ship design, plus vehicle design. Character growth in play is supported. Psionics are potent, but again, limited useage; utility further reduced by possibility of failure. Art ranging from mediocre to excellent, and usually appropriate.
TNE: Heroic PC damage taking, an otherwise excellent set of man-to-man rules, even more realistic design sequences, including weapons, vehicles, ships, body armor, and more. A closely related boardgame of ground warfare (Striker II), and the same large scale commerce rules as Ct and MT. Character growth in play can far exceed CG. Characters require significant conversions to work with CT/MT. PSionics unpredictable in effect, but no useage limit. Art almost uniformly good.
T4: again, a fairly bland ruleset. The rules for Craft designs have severla layers of abstraction available, and are based off of a more broad superset of the TNE technical architechture. There is an alternate vehicle design sequence. All the technology options of TNE, and more. 3x the skills of MT, 4x the CT skill levels, but compatible attributes, and adding a way-faster-than CG character advancement. blenty of support materials. A large scale political simulation supplement. More Psionics options than any other edition, and the most potent psionics rules so far... reliable, and useable often, but again, useage is limited. Great layout, goot to excellent art, bt often innapropriate to the materials at hand. (The Elmore pencils are exquisite, IMO)
T20: CT compatable ship design, expanded a bit, and a similar vehicle design system. 3 damage systems, each nearly identical, for three different scales. Characters incompatible with other editions, and a strong growth system. Lots of support. Small scale commerce rules. A very different, but playable and not overpowering psionics system. Layout clear, art good to excellent, almost always on target.
GT: a simulationist engine with strong gamist elements, which draws simulationists and munchkins in dispropotionate numbers... due to the GURPS technical architecture, wide ranges of technology not prt of the setting are available to GM's. A simulationist trade system available, with detail levels which produce trickle-down effects in the setting. Layout good, clear, and art good to exquisite, sometimes art used makes no connection to page, but usually appropriate.
Traveller 2300: Incompatible characters. Technical Architecture for ships only. Different hyperlight travel. brutal personal combat. semi-official conversions to use another company's game to resolve larger combat actions. Starships developed in a separate boardgame. Not part of the same "history", so compatability not made an issue. Uniformly good art, nice, clear, readable layout.
Now, confronted with the whole range, what do you teach to new players? Whichever you're using, usually. If your players are GURPSies, GT becomes an obvious choice. If they are D20 fans, T20. But, until this summer, new players would have trouble aquiring thhe base rules for anything else besides the "Current" rules. Now, they're all available in one form or another, leagally and (Except GT and T20) relatively cheaply.
The wide range of setting and rules issues is a problem. One which is probably going to be an issue for years to come.
by the same token, players now need to know the differences. So any "Setting Overview" needs to make clear that the systems differ, and that 2300 is a wholly different setting, GT is a side-branch (and has some different assumptions due to the nature of the GURPS version), and CT, MT, T4 and TNE are not supported, but are available. Mention of T5 would probably be a bad thing, unless it actually appears for sale.
Traveller is attracting new players, and new fans; It could be attracting more, but the issues that cause the problem are unlikely to be resolved: rule-set choices and setting choices. A good introductory ruleset (say CT-lite, like hunter mentioned) which references the range of options, strengths, and products would be a favor to new players. Something that also presents a good overview of the settings available, and makes it clear that Traveller is a living entity, with more choices than any other multiverse in print.
Perhaps MWM should put up such a page at his website... If people know ahead of time the various rules-styles, they can pick the one right for them and their group.
And Hunter, Dual-stating is a good thing.
