We use Perforce here at Ubisoft and previously at Radical, and pretty much all the other large studios I know of use it too. It’s also free for up to 20 users (http://info.perforce.com/free.html) – I’d seriously consider using it if I was setting up on my own.
I haven’t used Git much more than just installing it one day out of curiosity. I know that it’s the most popular among indies and seems to be the way forward in terms of workflow (Perforce is trying to do something similar with streams, but I haven’t used that feature so don’t know how successful it is), but I also know that the large binary file support in Git is not great. That was a while ago though, it may have changed since then.
The other advantage of using Git is that you can use Github to avoid setting up, maintaining and backing up your own server, which you would have to do with Perforce. It also facilitates distributed teams much better than Perforce does I’d imagine.
There’s also Mercurial, but Git seems to be winning that particular war.
I know nothing about Unity’s Asset server, except for hearing bad things about it from various places.