Actually, well cut asschers have shown to have light return that would rival a well cut RB. Especially colored light.I'd go for the round. It has far greater light return and is much sparklier, whereas step-cuts like the asscher has more of a glow to it.
And here is a good read on size comparisons when it comes to Asschers and RBs
Honey I Shrunk Your Asscher Urban Myth
The difference isn't that huge.
With all that said, they're both such different looks.
I consider both to be classics.
You have to choose what makes your heart stop.
I have an Asscher e-ring and I love it. I've seen some RBs that were stunning, but that shape didn't call out to me the way the step cuts did.