I love the Europa Universalis series (and similar Paradox games - Hearts of Iron & Victoria). You're right - EU is complicated, and does have a steep learning curve. So, if you're looking for some instant gratification, EU probably won't give you that. But, the complication is part of what makes it fun, and I find it to be worth the effort. (This is also why it is hard to pick something that is comparable to EU but also simpler - complex detail is partly what defines it.)
As for alternatives... well, the campaign mode in the Total War series is a lot less complicated. You can auto-resolve a lot of battles if you don't want to get down to the battlefield-level nitty gritty all the time. Still, it's not the same kind of game as EU. (Don't get me wrong, the TW games are great - Rome: Total War is one of my favourites of any genre; but different from EU).
There's also King Arthur - but it is more like Total War than EU. It adds some interesting RPG-style elements. You could try
Hegemony, which has a slightly different take on this sort of strategy game (seamless transition from board-game-style overview map to the battlefield). But now I've strayed pretty far from EU. :P
Hopefully someone else has some better suggestions for you. I'd love to discover some too.