Actually, Avonex is an intramuscular injectable, and it is only once a week (and with a larger needle).
You write "they don't reduce the rate of progression to disability" but I'm not sure their efficacy in that regard has been proven or disproven.
Okay, first of all, both of these drugs are interferons. That means that it modulates the immune system response to reduce the number of relapses. Both drugs are sub-cutaneous injectables, which means an injection every other day with a very small needle. (This may sound terrible, but it's not so bad. The injection is painless.)
I've recently become disenchanted with interferons in general, especially Betaseron. They don't reduce the rate of progression to disability, although they still have about 15-30% reduction in relapses.
When I was first diagnosed, I started on Copaxone, which is glatimer acetate. They don't know why Copaxone works, but they have noticed a similar reduction in relapse rates. I took it for 4 years, until my body developed an allergy to it. I had several relapses my first year on Copaxone, and a couple my second year, and started to gradually improve by the third year. It's been several years since I had a relapse. I then switched to Betaseron. Currently I'm not taking anything.
The other issue that your doctor hasn't mentioned is that some people with MS respond better to interferon treatment, and some respond better to glatimer acetate. You should probably do some research on the various drugs available to you, and what your insurance will cover. You should also ask why your doctor is recommending these drugs, as he/she may have a good reason.