The Drama Critics Award is about rewarding excellence (even though we may disagree with their choices sometime). The Tony's are about rewarding excellence when it is possible; and, when it is not, it is about doing what is good for business and rewarding something. There have been some pretty miserable seasons, yet most categories produced winners. I seem to recall that there was one year -- I think it was when Big River won -- when the Best Actor and Best Actress in a musical category were eliminated, presumably because there were no candidates or they were really bad.
In most cases, the awards were still given and a pretty undeserving show IMO was awarded, e.g., Big River (the competition was actually an embarrassment); Contact; Memphis (which I enjoyed); Passion (again IMO -- I know it has its fervent supporters, but when a Tony award winning musical closed after 6 or so months, that tells me something); Edwin Drood. (Did any of those shows really deserve to win Best Musical)? This season, without TBV, it probably would have been Mean Girls, because it is a hit.