Nolanverse is superior than DCEU in capturing the core of Batman, as well as making pretty superior films too (well...until Dark Knight Rises). Nolan not only captured the Caped Crusader, but I thought that Bruce Wayne portrayal was excellent. In fact, Nolan captured a fantastic Bruce Wayne and a pretty good Batman.
The DCEU just...I mean I liked Affleck as Bruce just fine, but I had a SEVERE problem with Batman vs Superman and then Justice League came out and it felt like they swung too far the other way. He was either TOO GRIMDARK BRUTAL BROODING or TOO SNARKY, FUNNY, HAHA LIKE TONY-STARK THE MCU IS A THING HEE HEE in the DCEU. They really just need to hone in on what they want out of the DCEU and Batman all together.
Personally? I still think the best Batman is the Bruce Timm Animated Series Batman. They just had it all going and when I compare Nolanverse Bat to Animated Bat, I think that Nolan took a lot of the personality and story notes from Bruce Timm.