I have the 2005 3500 Dually. i found most people said it was rated for 10-12K with weight distribution system. 5K without the weight distribution setup. Which seems really low (cover our ***** maybe is what Dodge was thinking). Since I have a 14K dump trailer and haul a couple of tongue heavy 10K enclosed trailers I upgraded my truck the the Torklift Super Hitch and have not looked back. My next truck (hope to get the 2010 3500) I will also do a Super Hitch in the 1st 100 miles. Torklift's Original SuperHitch
I found out the hard way, that the Titan (17000 lbs) I took off my 2006 3500, WON'T fit properly on the 2010 3500. We had to fabricate new supports, and shim the rear bumper out almost an inch. Worked out OK, but a lot of extra fooling around. I understand titan now has a new kit out for the 2010's. You might find that Torklift has modifications as well. Maybe you can sell your old one with the old truck and then not have the problem. I thought with the frame being the same, it would just bolt on. Not quite!!
Found this info in a 2004 Dodge Ram 2500/3500 Owners Manual I found online. Should be the same for 2003's.
With a Class III Hitch, your vehicle can be equipped to
tow trailers with a Gross Trailer Weight (GTW) of 5,000
lbs (2 268 kg) maximum. Factory-installed rear step
bumpers are rated a Class III hitch. Tongue weight must
be equal to at least 10% of the gross trailer weight (GTW),
but no more than 15% of the GTW.
A frame mounted hitch of up to Class IV rating, as rated
by the hitch manufacturer, is supplied as part of the
trailer tow prep package. With a Class IV Hitch, you can
tow a trailer with a Gross Trailer Weight of up to 12,000
lbs (5 443 kg) maximum depending on your vehicle
equipment. Tongue weight must be equal to at least 10%
of the gross trailer weight (GTW), but no more than 15%
of the GTW.