My situation is similar - leg weakness, balance problems, RRMS for about as long as you (dx in '95), all that fun stuff. Anyhow, I too was on Avonex for about 1.5 years, and my neuro suggested a switch to Copaxone (he didn't like what he was seeing on the MRI and didn't feel the Avonex was cutting it). I started Copaxone around May of this year. I don't really know how to evaluate it with regards to efficacy, but I do like that I don't have to put up with feeling sore and flu-ey from my meds anymore. I also have an easier time administering the Copaxone. The autoject rocks! Sub-Q is much nicer for me than IM. Anyhow, I haven't had any major relapses since I've been on it, and generally tolerate it well.
In any case, I think you should quiz your neuro about why she wants you to switch, especially if you feel the Avonex is working well for you. The answers may be compelling enough to convince you that a change in meds makes sense.
Did I mention that I really like the Copaxone/autoject combo?
Jason
(NOTICE: Your mileage may vary. Not available in all areas. See store for details. Insert favorite disclaimer boilerplate text here. Minimum balance requirement. Past performance is no guarantee of future results.)