Which webserver is much better for production for RoR hosting?

for instance: mongrel versus apache2?

can mongrel does something which apache2 cannot ?

mongrel is definitely an application server, while Apache 2 is really a web server. They are not rivaling one another, but cooperating.

With that said, you need to ignore mongrel and go have a look at Phusion Passenger, that is a credit card applicatoin server which will use either Apache or Nginx (another web server).