I am starting a new distributed project. Should I use SVN or Git, and why?
SVN is one repo and lots of clients. Git is a repo with lots of client repos, each with a user. It's decentralised to a point where people can track their own edits locally without having to push things to an external server.
SVN is designed to be more central where Git is based on each user having their own Git repo and those repos push changes back up into a central one. For that reason, Git gives individuals better local version control.
Meanwhile you have the choice between TortoiseGit, GitExtensions (and if you host your "central" git-repository on github, their own client – GitHub for Windows).
If you're looking on getting out of SVN, you might want to evaluate Bazaar for a bit. It's one of the next generation of version control systems that have this distributed element. It isn't POSIX dependant like git so there are native Windows builds and it has some powerful open source brands backing it.
But you might not even need these sorts of features yet. Have a look at the features, advantages and disadvantages of the distributed VCSes. If you need more than SVN offers, consider one. If you don't, you might want to stick with SVN's (currently) superior desktop integration.