Wow. Waxbanks should spark some discussion with this one...

The Dead always struck me as traditional songwriters where a large body of their songs had simple chord structures, A/B song structures, and a high level of accessibility for the album versions. While these were often blown to the wayside in concert, the core of the Grateful Dead was Americana music (bluegrass/blues/folk) which they were able to challenge with their live interpretations.

Phish, OTOH, had extremely challenging song structures, often times doing everything possible to keep from having a chorus. Fugues, counterpoint composed sections with little or no lyrics made for a need to work much harder to understand the musical expression in the song. More of how a symphonic piece is appreciated vs an AOR single.

From a live standpoint, Phish always seemed to have more of a Jazz sensablilty than the Dead, focusing more on tension and release than chaos vs order. Having only one or two members dropping LSD at any one time vs the whole band just may have something to do with it as well.