The truck has to tow the trailer load and do so in a manner that is not nerve racking and allows a margin for emergency maneuvers and fast stops and for safe merging onto a freeway and into traffic.
What is overlooked all to often is that the gears are as important as the engine in determining tow capacity. A GM truck with a gas engine and the 4.10 gears has 25% greater towing capacity than the same truck with the same engine and 3.73 gears. This is clearly shown in the towing guides from the manufacturers.
The advantage of lower gears is in more towing capacity and also in being able to accelerate faster when merging with traffic or overtaking a slow big rig on a steep grade.
12,000 lbs. is the point at which a diesel engine with its much greater torque is warranted. Below 8,000 lbs. a gas engine makes more sense. At 10,000 lbs. you can go either way. The advantage of a F-250 over a F-150 will be a stronger frame and better brakes which will provide more of a safety margin for someone towing constantly. For occasional use the F-150 with the right engine and gears and with a weight distributing hitch and anti-sway bars will work just as well.
One last thing to consider is the fuel tank capacity and options for adding an auxiliary tank or replacing the stock tank with a larger one. It is nice to have a couple hundred miles more range when towing.