The F-150 should tow it fine. The only difference in the F-250 is that the curb weight is about 700 pounds more. It might offer a little more stability.
The fuel mileage might be close, the 2011 and later F-250 will come with the 6.2L gas or a 6.7L diesel. Sure the diesel will get better mileage than the 5L while towing or driving solo, but the $6,000 - $8,000 additional cost will never be recouped by driving even 15,000 miles a year.
I would keep the F-150, and not upgrade unless you are going to tow more than 10,000 pounds, or the GVWR of the loaded F-150 is being exceeded. You might have a light duty or heavy duty F-150. Post the GVWR on your drivers door, and we will be able to tell you if you have the heavy duty version or not.
If you change, just to increase the payload, think about a F-350. It has a 4,000 pound payload (+- 300 pounds) while the F-250 is close to 3,000 pounds, and the F-150 with heavy duty package and ecoboost engine has closer to 3,300 pound cargo rating, mainly due to the lighter engine, transmission, frame, and overall a bit smaller than the F-250.
Fred.
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