I've been an hg fan for a while and like it better (hg jives with my brain better and git occasionally throws weird problems at me) but quality wise I can't say there is much of a difference in my experience.
That said, I have never met a single other person who uses hg. Not at work or hackathons. Most have never even seen an hg repository and some haven't even heard of it. Git definitely has "won" this "war".
The problem is that large swathes of the Git community have been treating the whole DVCS scene almost in Hunger Games terms -- there can be only one winner, and all the others must die.
For what it's worth, I've heard quite a lot of anecdotal evidence that Git is pretty contentious among many teams that adopt it. Git adoption is often driven by an aggressive few, against the wishes of their colleagues who can be quite unhappy about it. Case in point: Git has more "hates" on amplicate.com than Subversion and TFS put together -- and "hates" outnumber "loves" by something in the region of four to one. (http://amplicate.com/hate/git)
(For reference, Git and TFS have roughly similar market share in the enterprise at the moment, and Subversion is about twice as widely used as either of them. Source: itjobswatch.co.uk)
I use hg for personal projects, but I agree that git has become almost a standard, and, as others mentioned, almost synonymous with the distributed version control systems. My feeling is the differences between git and hg are smaller than the advantages of switching from one to the other and reconditioning yourself to a slightly different work mode. (I guess I should have said "reconditioning myself".)