Seems to me that the actual highest percentage shot at a big buck would be the first week of bow season especially when it's still hot.
Bucks are sluggish and lazy in the heat like that and if you've been consistently maintaining a corn pile all summer long and get pics of them right at dark at said pile every night then it really can't get much easier.
This method is expensive and time consuming because you constantly have to purchase corn and keep it out all summer but seems to be the most effective way to kill a big one.
As for the rut, movement is erratic and random in my experience. you can either hit it perfect and see bucks running wild or it can be just like another boring December morning. Very hit or miss in my experience AND 200 yards in the wrong direction and you can miss ALL the action.
That said. 95% of bucks I have ever shot have been the last week of January. in the height of the rut. out of the same tree. in the same creek bottom. but if I could afford corn and would take the time to keep the field baited I could see where that could change.