I haven't tried Compile, but your description reminds me of Sorcerer from Wise Wizard Games. It is similar to what you described. As part of setup, each player picks a character, domain, and lineage deck and shuffles the three together to get a deck to play a tactical card game.
The game itself is fun. You always have options for what to do on your turn but never enough actions to do everything. The deck modules each have a distinct identity and abilities, creating satisfying asymmetry.