Which engine you have? 6.0, 8.1 or duramax? If 6.0 w 4.10 gears, it will be slightly noticeable, but nothing major in the power dept, with the others, I doubt you will even feel it. As for sway, there can be more, but use the right tires and you will be fine. Of course they should be 10 ply tires and when aired up properly, I doubt you will notice any real difference.
I have had several sets of 285s on my tow rigs, including the current one, and had no issues pulling travel trailers, tractors, equipment, stuff weighing twice or more what the tt weighs, you name it.
I will say that unless you really need the mt, get a somewhat aggressive all terrain instead, they do handle better on pavement. Also, the selection of 10 ply MTs is somewhat limited.
2010 Cherokee Grey Wolf 28BH
86ish palomino slide in
2000 F250 superduty 4x4 7.3/6speed crew/ short