To answer your direct question, fermentation will take the same amount of time, regardless of batch size, assuming you pitch a proportionally appropriate amount of yeast. If you tried to ferment a 15 gallon batch with the same amount of yeast that you would use on a 5 gallon batch, you will notice that it takes longer (also there may be other problems). But if you pitched that same amount of yeast into a 1 gallon batch, you would likely blow the airlock out of the top.
Dry hopping results will occur just as quickly, but again, it will require a quantity of hops proportional to the batch size.
The major difference is in heat application. The larger the batch size, the longer it will take to heat water and cool wort.