The Rebel comes with 18" wheels. For some reason, FCA used brake calipers in the Ram 1500 DT that don't fit most 18" wheels. It is unclear if there is a difference in shock absorbers. The Rebel is labeled "Bilstein-branded shocks".
However, if going off-road is the issue, The Power Wagon is the answer. It isn't that much more than a Rebel and all the mechanical bits are available on a Tradesman for less. It has 17" wheels and the same 33" OD tires stock. It has front and rear lockers. The suspension has more ground clearance, articulation, and angles of approach/departure than a Rebel. It has a front camera (I think). If you order the towing package you get the real deal with both parts of the mirror power adjustable, power folding, cameras that give you a side view of the trailer, attachments for two trailer cameras, etc. While the payload and towing are way below typical Ram HD levels, they are still better than most Rebels. People add aftermarket air springs or Timbrens to raise the limit. I believe 35x12.5 tires fit without issue and 37"x12.5 with a little trimming. With the 17" rims the 35" tires have 9" sidewalls. There are some serious off-road parts available for it.
Negative? Well, although the interior is updated some parts are still dated. The CC rear seat is much tighter than on the 1500 DT. Unventilated black leather seats don't seem like fun on a truck that could be in the hot sun all day. And no 4-wheel self-leveling air suspension, which is a big boon to just using it like a truck (e.g. lower bed height when loading). And it is a rather big truck for off-road. It may be an XL size Gladiator (for less $$$ than a Gladiator), but many off-road trails aren't XL size.
For 90% of buyers (and maybe 99%), the 1500 DT Rebel is still the better choice.