There's actually 8
if you include the discredited, unused and largely forgotten, first edition of High Guard (leper, outcast, unclean) which contained several unique and interesting concepts.
To add to what has already been listed, Book 2 ships were small and their size and performance were further limited by tech level.
Combat was map-based (miniatures, really) and weapons were limited.
High Guard blew the lid off of ship size allowing designs up to 1 million tons as opposed to the 5000 tons of Book 2.
Combat was abstracted (but it needn't be, as Mayday made provision for HG ships) and a huge variety of weapons and defenses were added.
Small craft design was added with High Guard, too. Book 2 was limited to off-the-shelf small craft.
MT is based on HG but adds more complexity in the design system and in combat options (sensors, for one). It also pushed the tech level out beyond Traveller standard and allowed for a new series of weapons and defenses.
I'll leave the other systems to those with more experience of them.
edit:
Combat system differences: A major difference between Book 2 combat and other versions is the computer rules. In Book 2, deciding which programs to run in the computer (and which programs you had available to run) is a major part of the combat system. High Guard and MT abstracted the computer to a simple die roll modifier. Missile movement and damage are quite distinct in Book 2 but, unfortunately, poorly defined. The boardgame "Mayday" clears up most of Book 2's inconsistancies and there was a Special Supplement in one of the JTAS isues that finalized the missile rules. Missile movement in HG is abstract.
Book 2 is very much a tactical game; trying to run several ships or resolving the fire of large ships, can be a headache.
HG (and MT) make dealing with larger vessels easier and make squadron/fleet actions much easier.
Trillion Credit Squadron (TCS) is a HG supplement which has a table in it that makes resolving the large numbers of die rolls easy to handle.
Design system differences: Book 2 basically uses a modular method. Most systems are taken from tables and added to the design. There is very little math involved and it's quite simple.
HG and MT are more complicated. They're still relatively easy to do by hand, but there is more calculation involved. There are spreadsheets available to handle these designs, so that might not be an issue.
