I’ve been on both.
I originally chose Copaxone because there were no flu-like side effects and I didn’t want to risk missing taekwondo training on injection days. It worked really well for me for 3.5 years (only a couple of very minor blips). It was dead easy to inject and, because it’s every day, you just make it part of your getting up or going to bed routine. Injection sites were a bit stingy for a very short time and left red blotches. I used to get lumps from time to time that took a while to go. Overall, I was very happy on it.
Unfortunately, I started a big relapse in 2009/10 and my neuro took me off it because he reckoned it wasn’t working for me any more. I then had my worst year ever
After a lot of faffing about with the neuro, I started on Rebif44 a year ago. The Rebismart autoinjector is pretty snazzy, the needles are superfine and the injections are easy - easier than Copaxone in my experience, although the bruising is worse. Side effects in the first few weeks were negligible because the dose is low. When I hit the 44 dose, I started having quite bad flu effects. I can’t take ibuprofen (which a lot of people say is best for the “flu”) and, while paracetamol helped, it didn’t get rid of it. I considered stopping at one point, but knew it was better to stay on it so did. I’m very glad I did! I had a mild relapse a few months after starting Rebif (before it’s fully in your system), but since then I have just got better and better! No relapses, plus more energy, less symptoms and I’m reducing some of my meds accordingly. (To be fair, I’ve also been going to the gym so that’s bound to be helping too.) The flu effects were manageable by 5-6 months and I hardly notice them now - I just make sure and take 2 paracetamol with my injection and then 2 more 4 hours later.
Btw, the reason I chose Rebif44 is that recent research shows that it is the most effective of the injectables. A lot of neuros tend to prescribe Rebif22, a lower dose version - the side effects are less on it and, while Rebif44 gets better results, the difference is not huge.
As far as choosing which one to go on, it really is a personal choice and there is no “right” choice. The msdecisions site has a tool for comparing the DMDs versus your preferences - have you tried it? It’s a great website.
Whatever you choose, I hope it works really well for you.