I can't speak to Copaxone, because I've never used it. I have, however used both Rebif and Betaseron, and the injections aren't bad, at all. It's done subcutaneously (just under the skin), and around slightly fattier areas, I hardly felt it at all. Unfortunately, I'm allergic to Rebif.
My symptoms were progressing at a fairly rapid clip, so my neuro got me onto Tysabri. I've had some 20 infusions, now, and for me, it's great!