I tried out the Rome and Europa Universalis games. They seemed to have great depth as empire management games, but I never got into them because combat felt dull: grouping up your armies from your provinces into 2-3 big stacks and attacking. I never touched Hearts of Iron III thinking it would be the same.
HOI3, if anything, is less.... visceral than that. While I love the game, the combat is, if anything, more a heavily abstracted and number based than the EU games.