Trying to use a different transmission will likely involve major issues with:
* Bellhousing: The bolt pattern and overall design won't match.
* Input Shaft: The diameter and spline count will be different.
* Output Shaft: The size and spline count will likely be incompatible with the transfer case.
* Clutch Hydraulics: The master and slave cylinders might not work with the new transmission.
* Wiring: Some transmissions have electronic components that may not be compatible.
In short, stick with an AX-5 transmission when replacing the manual transmission in your 2006 Jeep TJ 4-cylinder. Anything else will be a very difficult and expensive undertaking.