It's hard to really compare anybody to GD, and here's why. What they actually accomplished, I feel, is the creation of a distinct, complete, and complex musical language, which for decades has been refined and become even richer. It is a language that lends itself strongly toward interaction and unique ornamentation. There are many groups putting out great original music, but a lot of them are still deeply rooted in more traditional musical languages (which I feel are relatively simpler languages).
There are only a handful of other groups that have really paved entirely new and distinct musical languages. When I think of other groups that have done that, I think of groups like the Beatles, Little Feat, Pink Floyd, etc. None that I know of have created one as rich and complete as the Dead, though. What newer groups have ventured into that territory? Possibly Umphrey's Mcgee to a certain extent? Would be interested to hear any other suggestions for newer groups that fit that type of criteria.