I've actually never played Wesnoth, although I've heard good things about it. I want to say that combat plays out more like the Civ series rather than having a dedicated "battle screen" you'd see in HoMM - at least based on the gameplay footage I've seen [1].
OTOH, can never have enough turn-based strategy games though so I should give it a shot!
Wesnoth is great if you like games where you have to create and exploit situational advantages. Using advantageous terrain, the day/night cycle, and varied unit types makes it one of the most tactical games I’ve played.