there's no such thing as "AN" F150, there is a huge range of differences in trucks, and what they can tow, "150, 250, 350, " is about what cargo can go in the bed, and the springs and steering can deal with. It has zero to do with towing. AN F150 with 331 gears and a 4.2 V-6, can't tow 3000 lbs very well. My last F150 had a 5.4 HO, 4.10 gears, and max tow package and could tow 10,000.
If you are shoppig for a 150/1500 and plan on towing you really have to pay attention on installed options, most importantly which engine and rearend it has. Something used dealers generally never know, or will lie about. You need to be able to pull the axel codes and look them up.
On the other hand almost all 250/2500's are set up for basic towing up to around 8000 lbs.