it's quite subjective really. I have this pedal which is a clone of the "way huge red llama". It seems to be considered a fuzz pedal, but I tend to use it for the lower gain settings which are just like a light overdrive (as opposed to fuzz). Out of all the dirt boxes i've tried, this one is the most "transparent". No low end loss, no mid cut.
again, it could be how it reacts to my basses or my playing style or whatever. It'd be good if you could get to a shop and try out some for yourself.
Another thought - Once I thought I wanted more drive from a dirt pedal, but actually I was getting enough, I just needed to boost those dirty frequencies more with EQ, so rather than using a pedal in front of the dirt box to boost it into higher gain, I used an EQ pedal after the dirt box to give me the impression of higher gain.
Much of this will make little sense as i'm rambling at light-speed... yours is the last task of the day before I get the f*** out of this swealtering offce. Ta ta!