I'd say that the saturated, super high gain thing is mainly Dual Recto territory, but the Mark I was used on Weezer's blue album, and it's not whimpy either.
Marshall's TSL-100 or DSL series will get gain similar to the Mesa Dual Recto, but it's got more of the Marshall chunk on the low end.

For an example of DSL tones, check out Allison Robertson's playing on The Donna's
Spend the Night CD. Check out Our Lady Peace for the sound of a TSL-100.
However, I can get tones exactly like what that guy's getting with a solid state amp. I think that solid state is a bit more versatile for high-gain sounds than tubes. Tubes are too smooth for some things.
