[Master Belisarius]

I only can remember tree advantages of Stars! over Se3:
1) Better options into the Race design.
2) Simultaneous turns in multiplayer (much better to speed up a PBEM game).
3) The post-battle viewer for PBEM games (in SE3 you can not see how the battle was: only the result).

About the advantages of SE3 over Stars!, well, the people in the others Posts said most of them:
1) Better game setup.
2) Better ship design.
3) The combat simulator.
4) Less micromanagement: in Stars! is a nightmare keep your transport moving the resources.
5) Much better AI.
6) Tactical combat in solo game.
7) Although SE3 have not great Diplomatic/Espionage options (SE4 is much better), still is much better than Stars! (nothing!).
8) More cool components in SE3 (Star/Planet destroyers for example).
9) The way that SE3 managed the solar systems.
10) The Warp Points give a lot of strategic options in SE3.
11) The tech editor, and the capability to customize the picture of your ships.
12) Mining the planets decreases resources, and not exist a game option to change it.
13) Have a better game interfase (God, I love the SE3 right click menues!).

Overall: I only have played during some weeks Stars!, and in the other hand, still I'm playing SE3 after 2 years and 9 months!!!