I'm not sure that's generally the case, though I'm sure it does happen.
My dad and my uncles (all born in the 1950s and 1960s) were serious Deadheads. They've gone to over 100 Grateful Dead shows a piece. None of them really have any fondness for Phish, but I have no idea why.
I know my anecdote can be countered by several of the opposite side, but as a laymen to jam music, I can definitely hear a very fundamental difference between Grateful Dead music and Phish music.
None of them are ardent followers of a particular band. I know they still go see Phil Lesh and Friends or The Dead when they come around, and I think they've been to a few Dark Star shows.
They all had a heavy lean to the Blues/Country side of things, so they're all big fans of Steve Earle and the like.
They all got together to go see Mark Knopfler and Bob Dylan recently, and they all went to Van Morrison a while back.
EDIT: I think it's important to note that my dad was so distraught by Jerry's passing that he took a day or two off of work and sat around listening to old shows on cassette tapes.
My dad and my uncles (all born in the 1950s and 1960s) were serious Deadheads. They've gone to over 100 Grateful Dead shows a piece. None of them really have any fondness for Phish, but I have no idea why.
I know my anecdote can be countered by several of the opposite side, but as a laymen to jam music, I can definitely hear a very fundamental difference between Grateful Dead music and Phish music.