SVN's branching is as free as Git's. It's just a bit of housekeeping data that says where the branch starts, no changes to the stored files whatsoever. A 'copy' in SVN is like adding a symlink to a Unix directory. Note that the SVN branch will not require a network trip until you commit your working copy changes (but there's not much point having a SCM if you don't commit off-local at some point). 

Note that a Git branch will also involve some housekeeping - like adding that tag internally - that will have to be stored somewhere when you commit. It's not a big deal at all, which is why it's called 'free'.