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I'm not a complete expert with TI2, and know hardly ANYthing about TI1. From what I can gather, though, TI2 is roughly similar to TI1, whereas TI3 is a major revision.
In TI2's base set, there were only six races: Sol, Hacan, Norr, Letnev, Jol-Nar, and Xxcha. The Yssaril and Mentak were added in an expansion. The L1Z1X were only present as events that could occur (they were not a playable race). The Naalu were not present in TI2 that I can see. The Winnu, Yin, Saar, and Muaat are not included at all, either.
The engine is very different. In TI2, planets often have higher resource values, or very low resource values. But in TI2, unlike TI3, you don't "exhaust" your planet cards to build stuff. Rather, you get credits every turn, which you can save, or spend. Your credits depend on your planets and your TAs with other races.
The turns are very different, too. In TI3, it's a threaded-style turn where each person takes one action and goes around until everyone is done. The order certain things, like building and technology, can vary from turn to turn. In TI3, there's a set turn order: At the beginning, you have a political phase, then you get cards and credits, buy your units. Then, one player at a time, you move, then resolve battles; a player does ALL his moves and resolves ALL his battles before the next player does this. After all players have moved, you can then buy tech,place the units you built, and progress your "victory" stuff.
Victory in TI2 is also VERY different. In Ti3 you have objectives you qualify for, which earn you certain numbers of points. The first person to a certain number, wins. In TI3, there's a "progression track". The first person to the end of the track wins. Each step has certain requirements; early on, it's just to have a certain number of planets and techs. Later, it requires you to control a NUMBER of planets, as well as a number of resources and influence on those planets, all the while getting more techs.
The combat engine is roughly similar. TI3 has more units, though: Destroyers and War Suns are not in TI2. Restrictions are also different; Carriers only carry 5 things, for example.
I've only played a few games of TI2 compared, so I'm not close to being an expert, but my experience is that TI2 and TI3 have roughly similar feels, but very different implementations of it. So different, in fact, that it's probably possible to enjoy BOTH games, without feeling that one is severely lacking and only the other one is any good.