I'm going to pursue the friend of a guy I liked
Do you like him, as well?
It's not so much because I like him more than that I'm sick of the other guy
You can be attracted to whoever you like. You can pursue him, there's nothing wrong with it. Make sure you are doing it for the right reasons though.
I don't like the first guy, I can't wait to get rid of him.
Make sure you do it politely. End things with the old guy first and then approach the new one.