I've had both briefly and greatly preferred the BM to the Rat. I know the Rat has some strong proponents around here - particularly that wascally Wenzel fellow - but I found it way too much, too soon. The range of dirty tones that was useful for me was literally on the first 1/8 of the knob, and everything after that was a cartoon.
The Bad Monkey, however, is a really nice pedal with a much more usable range of dirt. The dual tone controls are what really make these pedals, though, since you can adjust the bass and highs independently.
My advice? Unless you're looking for metal, get both a Bad Monkey and a Digitech Screamin' Blues off eBay. You should be able to score both of them used for less than the Rat would cost you, you can A/B them to see which one you like better and then flip the loser back onto eBay.
This is exactly what I've been doing, and for my purposes I liked the Screamin' Blues much better than the Monkey. The Monkey was much warmer - too dark with my Filter-equipped Annie - and seems to add overdrive "around" your guitar tone, whereas the SB's grit seemed much more integrated into the actual guitar tone.
The BM seemed to have more sustain, if that's your thing, but I liked that the SB's grit decayed at the same time as a clean note would - none of that fuzzy-hanging-on stuff that sticks around long after the note itself has died off.
Also, Proteus posted a dirt box shootout a couple weeks ago that includes both these pedals. That should be your first stop.