Towing 2000 pounds with the 4.0 SOHC engine is not a problem. I tow my race car on a trailer with a combined weight of around 3500 lbs plus about 800 lbs of gear on the bed. I have climbed over the Rockies with it, and only had to shift into third on the steepest inclines. Sometimes traffic slows me enough on a steep incline that I have to hit 2nd gear to get back up to speed but that is not common.
Stopping is more of a concern to me and I have trailer brakes for that. I recommend them to anyone that tows significant weight.
I don't have experience with the 3.0 but I use to tow with the 2.9L engine. That was a lot more work on hills. I could not climb anything but a slight incline without having to shift to third and even second on the steeper grades. That was with 4.10 gears and 31 inch tires. I'm glad those good old days are gone.
2002 FX4 Bright Red Supercab 4.0 SOHC, manual 5-spd & Tcase, 33" BFG MTs, K&N air filter, Modified air box inlet, Gibson SS cat. back exhaust, Bama flash, Hidden Hitch round receiver, Rear helper air springs, Electric trailer brake controller, Line-X bed liner, WAAG bar with KC lights and Wildernest shell.