I've never tried a quad but do own a DC5 and MKIII blue stripe Simul. You may want to check the mesa site and read the manual for the quad as it does give some insight into the sounds they were shooting for.
I believe that the Quad is based on the Mark series so you can get gobs of OD/sustain and spanky to furry cleans. Myguess is that with the quad you are going to be up against huge variables in the power stage that could severely alter your tone. You could use a Mesa Simul 295 nd get one sound and use a Marshal EL34 based power amp and get the completely other end of the feel/tonal spectrum.
Now for the DC5, great cleans, can add a little hair as needed and a nice amount of give in the feel. probably the 6L6 power section. Oddly , I think the OD channel is very up-front in spite of the 6L6's. Big sound. still a very smooth distortion and dark tone. Playing this am in fact, I liked the boldness of the DC compared to the sponginess of the MKIII.
I don't know if this is any help but just observations. Again , not having tried a quad but having owned my 2nd MKIII simul,( blue and red stripe) I am familiar with the MK sound. As I mentioned, the quad's final tone is at the mercy of whatever power amp you pair it with.
Good luck in the search for the grail!
