EAW is more like a space 4X: it boils down to "kill the other guy(s)" but there's a distinction between the empire-level and tactical maps. I found it okay, although I liked the Corruption expansion more because of the somewhat unique flavour of the third party/pirate/independent faction, plus fleshing out that faction required that they add more non-movie/expanded universe ships and units, which is a Good Thing (I loved Star Wars: Rebellion for this, but that game is showing its age).
SoaSE is more like an extended RTS, think Starcraft in space (note that despite occurring in space, there's no controlled 3D movement, but EAW didn't have this either). There's only one map; empire management occurs at the same level as tactical combat. I think the original goal was to make it a kind of real-time 4X game but, in my opinion, it does not work out that way: the only options for victory are obliteration or mutually willing alliance. I find the pacing kind of bad because there's a lot of tedium in just pushing fleets around and glassing the other guys' planets, then taking them over so they don't take them back (though thankfully you can queue constructions if you have resources to pay for them in advance). This is especially true once you're done with research, which tends to happen quickly for me since I always play at fast pace purely because I feel the games take too long (especially in combat/movement) at any other speed. Likewise, once research is done and you're steamrolling, you've long past the point where you'll ever be concerned about resources. This pacing and the game in general is probably better in multiplayer. The races are more Warcraft-era than Starcraft in terms of how distinct they are, but they still have some unique research as well as unique powers (particularly in their capital ships as well as some support ships) to set them apart. Micromanaging these powers (especially in corvette and cruiser tier support ships) can be annoying since toggling auto-use is okay but not necessarily the best way to use them.
All that said, I haven't played EAW in a while (years), but still load SoaSE Rebellion (or rather, its under-construction mod Interregnum) on occasion. SoaSE is definitely more popular, particularly in the modding scene.