I have the Benzin, and it's fantastic. Without tons of switches, it has a very wide variety of tones.
It's extremely thick, and has a looser feel than many high gainers.
In the Ch3 - mode, it's like a hot rodded plexi.
Ch3 + mode is very open and great for 90's hard rock.
Ch4 - mode is more compressed, can do great Metallica tones here.
Ch4 + mode is very high gain, much more so than expected. Thick, and VERY heavy.
One thing I will say us that even though it's definately in the Marshall camp, it doesn't have that British grit that you associate with those tones.
It's way more open and smooth, which may be a plus or minus for you.
Like most, I haven't played the JJ Dirt, but I can imagine the Benzin is heavier and slightly tigher. Both will cover very similar tones.