Well, the commercial VPN may or may not log traffic, so let's say it's 50/50.

Your VPS, on the other hand, is your VPS. If the police comes to your server, the company has no reason to hide who you are. That's 0% deniability, they'll come straight to you as the owner of the server. You'll then have to prove somehow it wasn't you (and you were, so it's a tough one). At the very least you'll get lawyers involved.

LIke probably_wrong said. If you own the VPS and only your traffic goes through it, your deniability is pretty low. All the traffic emanating from the node is still "you", only translated.

They don't need logs on the box to track the activity of the box.

I have used both techniques discussed, mostly for being able to download stuff I purchased on iTunes while being over seas.