I have played both and I enjoy both, though I have played much more of EU4 than of Civ VI. I simply enjoy it more. The games are both strategies, but quite different ones. Civ feels like playing a chill board game to me. EU4 makes me feel like a ruler of an empire (republic, theocracy, ...) much more.
AI of EU4 definitely wins over the AI of Civ VI. If the Ottoman Empire declares war on you and brings a massive army to your borders in Civ, you still have a very solid chance of defeating them by using tactics, and if you need it, spit stream of units form your cities using production/gold/faith. On the other hand, if the Ottoman Empire declares war on you and brings a massive army (and navy) to your borders in EU4, a real struggle for survival can begin. The thing is, the AI will prepare itself to war, and it will calculate the chances of victory. If the AI declares war on you, it knows why it's doing it. And I can only say from my experience that winning a war against a great enemy feels much more rewarding than beating the AI in Civ.
In Civ VI, you can more or less apply a universal strategy to win, though it's true that each map will be different, and this will shape the game significantly. EU4 feels to me that while the map is always the same, I have to solve new problems each time I play. Each game, there will be different powerful nations, different borders, different rivals and different sets of alliances that are going to affect politics and wars a lot.
But I don't want to only criticise Civ. There are positive things about it, too. In Civ, I value the fact that there are victories you can pursuit - be it going to space or spreading your religion. Finishing of the game is quite rewarding. In EU4, there isn't any official ending victory. After you reach the end date, a table with stats and pieces of information about your nation will appear. The only goals there are are the ones you pick in your head (like forming Italy/Germany/Qing/Roman Empire/whatever, restoring Zoroastrian Persia, conquering the world, ...). Well, and like in Civ, there are Steam achievements, too.
And, as it has been already said, Civ is much shorter and time-friendly. It takes me two to four days to finish a game on standart speed. If you wish to play full 1444-1821 campaign, it's going to take weeks, if not more than a month.