OP
I have a 2012 F-250 lariat with the 6.2 and its loaded minus the nav. I tow a 9500# loaded fiver and it does excellent! It does in fact have a higher payload (2750#'s per the sticker in the door jam) than the diesel similarly equipped. I did have to add a leaf and installed Bilsteins as stock it squatted badly with the rig attached. It sucked that mods had to be done to get it to handle the load which is very much within the trucks specs, but I just wasn't happy with the squat and bounce with the factory set up. Other than this small issue, the truck has been fantastic and tows great. Between the two you've mentioned and the weights you quoted, the 6.2 will do a amazing job. Especially coming from the TV you have now.