See my signature. I pull our 34 Limited just fine with the '02 PSD Superduty. The Hensley hitch is great!
Sometime in late model year '01, the F250, with camper package, and single-rear wheel F350 became the same truck... all the same components. In early '01, the main difference was a slight difference in the rear springs. The late production '01 models that were upgraded have the '02's big bore fuel filler and can take the high-volume diesel pump nozzles. They also came with Gold coolant vs the green that had to have additive added every so often.
The GCWR of the F250-F350 is 20,000 lbs. The F450-550 are higher because you can get 4.56:1 gearing with them, not to mention their stronger chassis and brakes.
With the factory towing package, your hitch receiver should be rated 1250/12,500 lbs. Look for a sticker on it.
You'll be fine.