My two cents, for what its worth.
I have a DR clone that was already set up with beefed up Mercury iron for both tube types. Changing from NOS Brimar 6V6s to NOS JAN Philips 6L6 GWBs just broke up later. That said, the breakup characteristics are different, not one better than the other.
The output went up to about 33 watts, so I assume that 6L6s that are more powerful than GWBs, could potentially give you a few watts more. That might not translate into much more volume, and I doubt it will sound like a Twin - maybe more in the Vibroverb type camp. A tad fatter, but very hard to notice.
If you're thinking production tubes, I actually think that JJ 6V6S tubes sound very good, and may actually be somewhat in between a 6V6 and a 6L6 tone, and you won't need to upgrade your iron.
Srini