Having now visited through the tenure of three different GM's at my favorite Tokyo hotel, the Park Hyatt, I can definitely notice the effect of their different styles. But I am not so sure that I would have readily recognized the differences were I not a regular guest.
For a hotel where I am less regular, one key factor is whether the GM will hide in the unlikely event that I feel I need to talk to him or her. My view is that a GM who hides from a customer wanting to talk has a reason for hiding, and it isn't likely to be positive.
Which leads to the most inportant reason why the GM makes a difference: tone at the top. Can anyone look at the results of actions by customer-inaccessible airline top management and NOT say that tone at the top makes a difference? Hotels are no different.