KWT, you need to know the values for the new trailer. Also, keep in mind that you need to consider the weight of the personnel inside of the cab along with all their stuff. This is where the F350 has the advantage over the F250. The pin weight shouldn't be too big of an issue going to a slightly bigger trailer if it is only you. But, start tossing in the wife, 2 kids, a dog, all the camping stuff, etc and you can find that you can exceed the rear axle weight rating really easy.
Also, keep an eye on the frontal area of the newer trailer. There is a limit to the frontal area that the trailer can have (it is like 80 square feet or something like that). So, you may run into issues there too (little known rating for the truck, but it is inside of your owners manual).
You should be fine, but if you plan on hauling this around a lot, may want to consider upping the sway bar to a much larger size, say a 1.25 or even a 1.5" bar to help with stability. You will find that going with the bigger trailer on the lighter springs is going to lead to more sway. Sure, the truck can handle the additional weight, but can you steer it with the trailer swaying? Every driver is different. Can also install some load assist air bags which will help with the swaying as it will stiffen up the rear end by upping the air pressure in the bags when the trailer is on, but can lower the pressure down to around 5 psi (don't want to go to 0 due to possibly damaging the bags) to keep the ride comfort in an unloaded truck.
