I feel that I can be pretty impartial here. MMJ will probably win the poll because they are technically more accessible to the average person as they get a little radio play here and there while Phish gets none. Anyone whose main musical genre is jambands will laugh at that and say Phish, hands down. I have nothing invested in the jam scene and actually enjoy all genres of music (I mostly listen to a mix of indie rock and 70s soft hits) to a certain degree and I really like both bands. That being said, Phish is so much further ahead of MMJ it is not even funny. To even have a poll on this is sort of laughable. MMJ is a great rock band that meanders into jam band territory. They have a medium size catalog of songs and they tend to mix up their sets a little bit. I have seen them a couple times and they are pretty great live.
Phish, on the other hand, is an amazing live band. Amazing, not just pretty great. Their catalog of songs is probably 5 times bigger than MMJ, so any show they play is completely different. MMJ cannot touch that type of variety. As for the actual songs, MMJ has some true classics, but I prefer Phish's strongest songs over the best of MMJ. As such, when people are forced to put their money where their mouth is, you see that Phish routinely plays multiple nights of 25 - 35 K crowds while MMJ plays multiple nights of 1 - 2 K crowds.
Even if the two bands were equals, which they most certainly are not, the OP asked us to compare them as jam bands. One of the most pleasurable aspects of seeing a jam band concert is hearing random cover songs played during shows. In terms of covers, the two bands do not compare at all. Quite frankly, MMJ cannot even beat The Zach Brown Band in terms of variety of cover songs, because they do not really play many covers at all!!! WTF? Does the OP even listen to jambands? How can you be a jamband if you do not play any cover songs? I saw a Phish show a couple years ago where in the first set they opened with Bob Marley's 'Soul Shakedown Party' and later in the set busted out a full rocking version of Edgar Winter's 'Frankenstein'. MMJ would probably ##### their pants if anyone asked them to bust out two covers in the same set, let alone show. In the second set, they opened with 'Crosseyed and Painless' (Talking Heads), which any music fan would recognize as a great song and then washed it down with Zeppelin's 'No Quarter'. This all happened in one night. I am sure MMJ has played cover songs, but they do not play them with regularity as Phish does, and Phish has a breadth of covers from which they draw that is truly mind boggling.
This is not even a contest. Phish destroys MMJ in every way.