I like both, but my preference is turn-based.
Edit: But where do we put real-time With Pause?
Some of my favorites in each category.
Action:
Piranha Bytes games, especially Gothic 1/2, and Risen.
Demon's Souls and Dark Souls (Salt and Sanctuary, a 2D Soulsvania)
The Elder Scrolls: Morrowind, but not actually for its combat.
Dragon's Dogma gas very cool combat. I love the fact that you can climb on monsters.
Some of the Tales games have really fun combat.
Vampire: The Masquerade - Bloodlines, despite its combat.
Turn-based:
Arcanum: Of Steamworks and Magick Obscura. While I don't love this for its combat, I love it for everything else.
Final Fantasy Tactics probably has my favorite turn-based combat out there.
Final Fantasy V. Not my favorite Final Fantasy (those are VI and IX), but I always have fun with the job system.
The Temple of Elemental Evil. While some fights can be repetitive, the combat itself, and all systems present are unmatched in turn-based rpgs.
Divinity: Original Sin for its flexibility.
Jagged Alliance 2 is probably one of the best tactical rpgs out there.
There's a lot more for both types of games that I could add, but this is just an example that both types can produce excellent games.