Nolan by a lot. The chase scene was the weakest action part of BvS. Snyder did Batman's hand to hand combat better than Nolan though.
A Cosmic Experience:

It was beep
hot
, too.
There was very little sound from the man except for a continual series of moans. - Charles Bukowski

With the stain on the third toe of yr left foot and a drop of wine on yr new jeans?
Ballers, I put numbers on the boards.

Snyder by a long margin; the one where the owner of the star wars franchise shifts dirt by ferry one way then attempts to link all the passengers to a Nazi computer and they all get saved by Wonder Woman on the way home.
Basically wot I did today.
Burger Bro?

Nolan, by a small margin, but I prefer the car chase in Batman Begins.
The Hardest Thing In This World Is To Live In It

Well he was the one to stop the batmobile. But if he doesn't count, I still prefer Snyder's because of the soundtrack.

Superman wasn't involved in the chase scene?

Snyder any day. Superman was involved as well as that awesome soundtrack.

Nolan's chase is better not just from a technical and visual standpoint, but from a simple storytelling point of view. During the truck chase in The Dark Knight there was more at stakes, and we knew why this chase is happening. In Batman v Superman, the stakes were lower, and it was more confusing to understand what is going on (in terms of story). The chase in The Dark Knight was moving the story forward. The chase in Batman v Superman was just there for the sake of action. If it would've been cut out from the film, it wouldn't change anything about the story.

Nolan

Elle Fanning as Robin chasing a DC villain.I'd pay to see that.

.
=w=

A chase scene involving Elle Fanning is even better.

Well Nolan of course. Zack, while he had some cool bits, didn't show case the Batmobile, we barely had an idea how the vehicle moves because he was focusing too much on the destruction. But I did like the music, a bit bombastic but I loved the string section.
=w=

The chase scene from The Batman involving Ben Affleck as Batman and Elle Fanning as Robin.

Nolan

Nolan's chase scene is almost perfect.
The practical effects, the pacing, the sound design and cinematography.
The lack of music creates great tension, but when the score does kick in it's absolutely epic.
It's great and I couldn't fanboy enough for this scene.
Snyder's oh man.
It's essentially an obnoxious Transformers scene with Batman.
The lighting is too dark and hard to see at times. The soundtrack is loud and distracting. The explosions and CG are over top and excessive.
When people complain about Snyder's movies not being fun, THIS is what they're referring too.