The UFO:A titles are more Xcom inspired than spiritual successors. The overall theme and goals are largely the same: recruit soldiers, research new and alien technology, produce better gear and such for your men, build and improve bases, shoot down UFOs and kill or capture aliens until you're ready to take on the big final battle.
There are a number of differences, though: A more hands-on RPG system, including perks, territorial expansion and control, planetary resources, competing factions, a combat in pausable real-time, lack of destructible terrain...
The three games in the series also have a number of big differences between them, which makes them, as a series, harder to describe. Afterlight, outside of combat, plays very differently from the other two. Base management has an entirely different focus, you have your core group of soldiers, who you aren't able to replace, so casualties can't be afforded. Instead, you can research and produce robots piece by piece, with a number of different components you can mix and match to fit whatever need you have. The entire game is more scripted as well, with a number of events...
Aftershock, on the other hand, gives you three "races" of humans to use as soldiers, each with their own research options, equipment, and uses. It also focuses much more on diplomacy, as you gain access to the other human soldiers based on your relationship with their faction.
They aren't Xcom, but they are good, solid games in their own right.
