* Valve body: The valve body controls the transmission's shifting. Different years have different valve bodies, and a direct swap might lead to shifting problems or even failure.
* Computer control: The 2006 transmission is likely more sophisticated electronically than the 2001 unit. The 2001 Sierra's PCM (Powertrain Control Module) might not be compatible with the 2006 transmission's control signals. This would require significant wiring modification or potentially a PCM swap, which is complex.
* Torque converter: The torque converter might not be compatible.
* Input and output shafts: While generally the same, minor differences could exist, requiring adjustments or modifications.
* Case differences: While both are 4L60e, there might be slight case differences that could cause fitment issues with the vehicle's mounting points.
In short, while the transmission *looks* the same, it's highly unlikely you can just swap them without substantial modifications and potentially specialized knowledge/tools. You would likely need a professional transmission shop to assess the feasibility and make the necessary adjustments. Even then, success isn't guaranteed. It would be much simpler and less expensive to find a used 4L60e from a similar-year Sierra 1500.