I'm going to have to go against the grain here, but my order of preference is:
Davidson
Bergeron
Bauman
Marshall
Rationale:
Davidson: This was the version that made me like HS (I saw the Marshall version as a single digit-aged tot and didn't care for it, details later). It actually was the wild, manic atmosphere and numerous "tangents" the show went on that made me like the show. Put another way, it was what Match Game '90 should have been as far as the "onstage Hollywood party vibe" goes, and perhaps MG '90 was what HS '86 should have been as far as keeping the game moving along. JM J. Bullock I thought was actually funny, and I had never suspected that he was gay. Crazy as cats**t, yeah, but never gay.
Bergeron: Great revival, great stars, and Bergeron was the perfect straight man to Whoopi and the other celebs. Whoopi I think just went overboard in some respects, but I thought it was a great show, even though Whoopi's final 1-2 seasons was making the show tank, but it bounced back beautifully when the Fonz took over. I think if Fonzie took over one season earlier or TPTB gave HS one more season on the air (until 2005), then HS would've had a much longer run.
Bauman: Say what you will, but I thought MG/HS, with all its flaws was an orignal and novel concept and the merging of the two shows' formats was done brilliantly (why else would 'Net MG/HS Hour be such an Internet hit after all these years). Further, the elimination of the "no tic-tac-toe by default" rule was a good one, i'll explain should anyone ask. The two things that hurt the show was the caliber of celebs (mostly soap stars and NBC sitcom stars) and Jon Bauman, sad to say. If Marshall was at the helm and some better celebs was selected, the show would've had a much more respectable run. I like MG/HS on originality value alone.
Marshall: I want to say in no uncertain terms that Marshall's run was a great one and had most, if not all the A-list stars Hollywood had to offer. However for me, I thought the show was just a little too dry (read: its humor was over my head). As a kid, I always turned off HS for another game show on tv. As an adult, I have a much higher level of respect for Marshall's version, but it doesn't put his version ahead of his successors' versions.