We were in the same situation a year ago and ended up buying the Ram 2500 with the 6.4L.
We previously had a 2013 Silverado 1500, 5.3L, 3.42. I actually really liked that truck, except for the annoying suicide doors on the extended cab (it changed in 2014). I quickly realized we made a mistake with that cab configuration, having a young child in a car seat in the back. Having to always open the front door to open the back door was a pain. We should have foreseen that, but hey, we only had an eight-month-old when we bought it, so that was still all fairly new to us.
Anyway, we decided we wanted a different truck and I started doing a lot of research, deciding it made sense to step up to a 2500 or 3500. I read this forum and many others about the different brands and engines. We knew we didn't need or want a diesel, as we only tow a 7,500 pound trailer, and most of our unhitched driving is no more than 5-10 miles. We have a Honda Accord for running around and long trips without the trailer.
I did not like the interiors all that much on the F250, and I don't know if this is a complaint, but it seems like I see quite a few F250s towing trailers my size that seem to be sagging. Maybe it's just me, but I think it's noticeable and I don't see that on the GM or RAM trucks.
That left the GM 6.0 and the Ram 6.4, which, honestly, wasn't much of a decision. The 6.0 is a tried-and-true platform, but I think it is getting a bit long in the tooth. If they would put the 6.2 in the 2500/3500 trucks, we might have stayed with GM.
I don't have a single bad thing to say about this truck. The design and style, to me, is top-notch. With 3K of payload, we are able to put a rick of firewood in the bed and still tow the trailer through hills with no problem. I love the big cab, and they seem to have thought of everything. The little storage compartments under the rear floor mats? Those came in real handy when my truck was broken into and the idiots didn't know to look in those compartments. That kept my iBall backup camera, and some expensive knives and flashlights from being stolen.
We did get it stuck in the mud in April while camping, even with 4x4. This truck is heavy and it just sank, with mud halfway up all four tires. Fortunately, we were yanked out by a new 3500 Ram CTD, not a Chevy or Ford. ;)
With all of that said, I will still consider all of the Big Three when it comes time to buy our next truck. At this time, I think they all make excellent rigs with reliable powertrains.
Good luck in your search and congrats on the new trailer!