I play them both, and love them both. They're both strategy, but they're both VERY different kinds of strategy. Civ really excels in the building aspect. Envisioning your empire exactly how you want it, and making it happen is a lot more detailed in Civ and a bit lacking in EU4 which is a little more strict in what a nation is. still allowing the player to forge their own path, but not able to go quite so far from reality as civ.
And, perhaps not as important to some, but something I absolutely adore, Civ is just bursting with style and aesthetic appeal, everything looks and sounds amazing, it's like a festival dedicated to the celebration of history and our species. Civ's biggest weakness is diplomacy however...
... and this just happens to be Europa Universalis' biggest strength in my opinion. The political scheming, backstabbing, and intrigue that a game of EU4 subjects you to is absolutely amazing. All the different diplomatic states, casus belli system, the fleshed out sue for peace system... all of it is top notch and adds so much depth to the game. A big reason why people don't get into it too easily too I think. They start out as small isolated nations thinking that's a good way to learn the game as it will be a simple introduction, but really the best way to learn is to jump into the middle of the HRE, or onto one of the major colonial nations and just get inundated with everything going on around you.
They're both excellent games, I could understand not having time for both (or even one, for that matter), but alternating 1 game in Civ5, 1 game is EU4 gives the best of both worlds.