If your just worried about live sound, just use an SM58 and forget about the other 2. I've used the RE 20 and the SM7. The only advantage really that I could tell for live sound is that if you have a mic eater you don't get as much proximity effect due more to the design of the mic cage than the capsule itself.
I bought an SM7 thinking that I was going to get some magical sound in a live situation. I think there's a reason that most of the live recordings you see are still using SM58's and not RE20's and SM7's. Trust me you're not going to get blown away by either and there' not going to fix bad rooms as much as everyone says.
Actually I'm going to get killed for this probably, but I really haven't found the SM7 much of a go to mic for anything :( It needs a ton of clean gain to sound good apparently, but why spend $350 on a mic and $500+ on a good mic pre if you can get pretty damn close (in a live situation anyways) for $100 with a good ole 58? I think you can great recordings with a 57 and 58 and a good LDC. I bought a RODE NTK and that SM7 hasn't been used since.