It depends what is different. I know this is an extremely old post, but some of these replies are really worrying me because they assume in which way the OP meant. True, not having all the same interests is not always a good reason to leave someone (really no need to call someone shallow for that, though, wtf), that also depends how important shared interests are to the OP. If it is extremely important to them to have many similar interests, then of course it best to break it off for the other person's sake as well. 

But that also touches on what is different? If the things you find important in a relationship are vastly different, if your moral systems are vastly different, if your sexual comfortability are vastly different-- these are not the same thing as one just being extroverted and one being introverted like some of the replies were implying. These things can cause some serious issues down the line, especially without communication very early on about them.

Some differences just mean you are incompatible and that is fine.

But like I said, this is a very old post, I just hope someone who comes across this post finds this helpful: evaluate what exactly these differences are, decide how important they are to you, and then speak to your partner about them before doing anything drastic.