* Same Generation: Both the 2001 and 2003 Ram 1500s are part of the same generation (the second generation, often called the "second-gen" or "classic body" Ram). This makes them largely compatible.
* Axle Ratio: The biggest potential issue is the axle ratio. The 2001 and 2003 models came with various axle ratios (e.g., 3.55, 3.92, 4.10). If the axle ratios differ significantly, it might affect speedometer accuracy (requiring recalibration) and your engine's performance. It's crucial to ensure they're the same or very similar.
* Brake Components: While the overall housing should fit, there *could* be slight variations in brake components (calipers, rotors, drums). You might need to reuse your existing brake parts from the 2003 truck or verify compatibility.
* ABS: If your trucks have anti-lock brakes (ABS), you'll need to ensure the ABS sensors and components are compatible. This is a more complex issue and potentially requires specialized knowledge.
* Wiring: The wiring harness for the rear lights, ABS sensors (if applicable), and other electrical components might need to be adapted or swapped.
In short: It's *likely* to fit, but it's not guaranteed to be a drop-in replacement. You should compare the specifics of the rear axles from both trucks (axle ratio, brake components, ABS system, etc.) before attempting the swap. Consult a repair manual or parts catalog to minimize surprises and potential problems. If you're not comfortable with automotive repair, it's best to have a qualified mechanic perform the swap.