SotS notes:
Turn based strategy bit (Macroeconomic, not civ-style), real-time tactical.
More diverse factions. (Mostly in that each has a different way to traverse space.).
Design your own ships. (Always a big plus for me, even if it is more variations on templates than entirely new designs.).
Very Big Flagships With Lots Of Impressive Guns.
Time limit on battle duration (times out with a draw after some time pass, and 'some time' can be determined but is 2-3 minutes by default.).
Sometimes annoying ship AI, or lack of it, esp. with regard to cloaking/stealth.
Random tech tree. (Random bits are missing every game, so you can seldom get all the cool techs you want/like.)
Change from strategy to tactical mode takes a too long loading screen (compared to SoaSE which doesn't even 'change' between strategic and tactic mode.).
Definitely only MP for the VERY patient, even if it is simultaneous-turn.
More dramatic starting screen music.

SoaSE notes:
Seamless integration of battle and economy.
More user friendly fleet control.
Definitely more polished, better graphics.
More mod-friendly.
Sword of the Stars is great, in many ways, but what it is definitely NOT good at is multiplayer. Forget it if you want to play that, it'll take WEEKS unless you take out the tactical battles and go with auto-determined instead, and that's the good thing about the game. Also, SoaSE is definitely more polished in most departments. (Even if it could use a fix or two, but 1.1 looks promising in that regard.). I've played plenty of Sword of the Stars, and it is good, but it is also, even more so than SoaSE, made by a small-time developer without too much in the way of resources. I have little problem with the lack of polish, but many do. (It, too, has gotten better with patches. Lots better.).