I've written several production apps in it, and the unicode fixes in particular are a much easier, as well as little things like being able to do enums.
Ultimately, they really aren't all that different- I think the differences tend to be overblown somewhat on HN.
If the course/teacher you like only teaches using 2.7, learn that. You can pick up the changes from 2.7->3.4 on your own pretty easily once you know the basic language.
If you for some reason have to work on older version (for example RedHat still uses 2.6) knowing Py3 is not really an issue to program there. Of course few nice features are missing, but people seem to talk as if it is a completely different language for some reason. With Python 3 at least you have a nice more consistent language.
If you were learning Java, would you start with JDK 1.3 or the latest one?
If you're just using it for its own sake, or only for building things locally that either don't need to run anywhere else or only need to run where you have enough control to install your own Python, and you don't and won't need dependencies that aren't currently ported... then definitely start with 3.x. :)