I personally run 13 inch tires all the way around because that is just the way we build them. I dont know if it is a advantage or not. The 16 inch tires put down a larger foot print onto the track than the 13s. This may be a advantage, especially for some of us that are alittle on the larger size.
I just put my 16's on this past weekend. They gave me alot more side bite, and more traction off the corner.
I could really tell the difference. The track is made up of a coarse sand that packs decent when watered well.
My 13's stuck very well on a banked clay oval karting track, so on a track like that, the difference may not be so drastic, I will find out in a month or so.