The biggest difference is that Civilization is turn-based and Europa Universalis is not, which in and of itself changes the nature of much of the gameplay and strategy going on. Civ is a 4X and plays very similarly to other 4X games - SMAC, Master of Orion, GalCiv, Endless Space, Space Empires and so forth - the core of the game is working your way up a tech tree and building an empire from scratch which will outclass other empires either through culture, technology, sheer power or whatnot.

Europa Universalis lacks a classic "tech tree" and does not start you out from scratch. This is an empire management game, not an empire building game. Things like trading, economy and resource management, family management (you don't get one overriding "leader" to play through the entire game as you would in a 4X game) and so forth are given much, much more emphasis in a grand strategy than in a 4X.

Empires can and will crumble. Your empire can and will be cut in halves or thirds, not just by external sources but by internal ones as well. A multitude of different factions from within your empire will fight themselves and each other for power. In the case of Victoria II, politics, political parties and elections play a major role.

It's rather difficult to explain but really it comes down to it a.) not being turn-based, b.) not being tech-tree based, and c.) being much more about management.

Edit: Hux did a better job explaining