You can achieve equivalent things with both but that doesn't mean the differences are superficial.
Having used Git daily for a couple of years, and Mercurial daily for about a month now, I find there is a distinctly different feel to both.
My experience so far is that when collaborating in a centralised sort of workflow, Mercurial makes it more difficult to keep private development branches, without keeping multiple clones of the repository. With Git you have to be explicit about what you share.
So with Git it feels much less of a big deal to do casual hacking; maybe things you "shouldn't" be doing if it's a work project, for example. It lowers the mental barrier to trying out a new idea.
Since I like to be able to do whatever I want, on my own copy of the repository, and only share with others what I want them to see (and what is useful to them), I prefer Git because it seems to make this easier.
Another thing: I did get quite excited on first seeing Mercurial's Python API (since I'm a Python user). I thought I was going to have a great time writing extensions. Then I saw the warnings that the API is not guaranteed to remain compatible.
Since I'm lazy (a noble characteristic I think, having also been a Haskell dabbler at some point), I gave up that thought quite quickly and disappointedly.