I get it. The SM-58s tend to sound scooped in the lower mids, to me. I agree that the RE-20 is a very different microphone than the SM-58 family. The RE-20 was often used as a broadcast microphone at radio stations, where a warm presence was welcome. I was a bit thrown when you mentioned a 10 db cut with eq, I don't think it is that warm. The RE-20 will not have an upper midrange boost that SM-57/58 users are accustomed to. Some parts you record will need additional cut, others need to sit back in the track. Have you tried the RE-20 for background vocals? It is also great on kick drums, horns, and on instruments which need a bit of their upper midrange softened. Different brushes for different parts of the painting.
Nothing works on everything. Are you happy with the Beta 58 for your vocals? What would you like more (or less) of that caused you to look for another microphone? I am a baritone, the RE-20 has worked great on my voice when the track is acoustic and not too dense. If I need more cut, I'll move to a large diaphragm condenser or a dynamic with a midrange push and severe low frequency roll-off.
I think that the SM-58s tend to work better on tenors. Audix OM-5s work better for me live.
Galil