What kinds of sounds are you looking for?
If it were me, I'd take the GK over the Mesa...mainly because I like a punchy more mid present sound (which is why my Mesa is for sale and the Genz Benz isn't).
The Mesa has a lot of heft and it's got a bigger rounder sound as opposed the GK's more solid state punch. Of course I'm not a huge fan of the 1001's in the first place. I think the GK 800RB is the best amp that GK makes, followed closely by the 2001RB.
As far as both amps you are asking about, they are both versatile enough to cover just about any type of gig, they are both built extremely well, they both have good customer service, and they are both very loud amps. The Mesa can go down to 2 ohms though and it does have a well received OD channel that is footswitchable.
It basically boils down to whether or not you like a tube sound or a SS sound I think though. I've owned both amps so if you have any questions, feel free.
Dan