stick is nice that you can fish from the center of the boat. better balance if just one person. makes planing quicker as well. other than that I don't know any other advantages.
I think a stick steer is great for die hard fishermen. My dad has one & loves it. Once you get to and/or leave your fishing hole you don't have to keep going back & forth from your console or tiller. Everything is within reach on the stick, including the trolling motor. I personally wouldn't want one unless I could afford to have a secondary fish only boat.
I used to have a 15 foot aluminum boat with 25 horse Merc. It had a stick steer and it was a great little boat for bass fishing in skinny water. I stupidly sold it and now it is gone forever.