So, disclaimer: I'm a Mercurial fan.
There are two big things git has traditionally done better than Mercurial: lightweight branching, and rebasing. Both were possible in Mercurial using mq (plus qguards, in the case of lightweight branching), but the experience was rather clumsy. I didn't mind putting up with it, since, at the time the two systems came out, Mercurial was markedly easier to use than git. But, over the last year, git closed a lot of the usability gap, while Mercurial has held almost completely still, and that's resulted in a lot of arguments that Mercurial's time had passed, and git was the way to go.
The good news is that this release fully eliminates git's first advantage, and either eliminates, eliminates and beats, or fails to address the second, depending on where you're coming from. The easy news to process: the rebase extension enables full git-style rebasing, end of story. You can do an automatic pull and rebase via `hg pull --rebase`, if that's what you want, or you can do more customized rebasing via `hg rebase`. So that's done, and, based on my use in production environments, works very well.
Now, Mercurial 1.1 introduces real lightweight branching--no mq hackery--via an extension called `bookmarks`, which ships with Mercurial. These provide identical capabilities and benefits as git's local branches. The complicated discussion we can have revolves around bookmark semantics. bookmarks, like git branches, are basically "floating tags"--tags that mark a head in the repo's DAG, and that move with that head as you issue additional commits. The difference comes from the fact that bookmarks very directly expose what's going on, whereas git's branch command hides what's going on behind what I personally feel is a more intuitive UI. So, the argument is: is exposing what's actually going on better, because it gives you more power; equivalent, since the functionality provided is identical; or worse, because too much implementation is exposed in interface. I personally need more time to sort out preconceived bias of what micorbranching should look like, from the bookmark extension in particular.