Two very different types of pedals. It depends on what sound you are going for entirely. A big muff, IMO is only good at sounding like a big muff. So if that’s the sound you want, its the best thing going, especially at its price. Single notes sound good, chords sometimes lose definition, depending on how you have your amp set up. Its a wall of fuzz, for better or worse. I’ve been using muffs off and on for years now and I’ve yet to find a truly satisfying all around tone with it.
On the other hand, I consider rats to be among the most versatile dirt boxes out there. I’ve never tried a you dirty rat, however, my vintage rat can have a wide variety of tones dialed in to it, all very responsive to volume controls, pickups, and the amp being used. I can get a dirty overdriven sound all the way to relatively fuzzy. It will not get as extreme as a muff, but it’s not supposed to. Its easy to keep chord definition and play lead lines.
My advice though…try them both out a local store. You can nab either relatively cheap on ebay as well.