All XLS models were made for the US as 01-02 year models. 4 speed transmission and manual transfer case (2H-4H-4L) with 4.9 differential gears, and the 3.5L engine. Various options and packages have been found on these, depending on the dealership that first ordered. Some can have the hybrid LSD as an option. 16 inch wheels
All Limited models in the 01-02 model years have 5 speed transmission and Super Select 4WD transfer case (2H-4H-4HLc-4LLc). These will have 4.3 gears and the 3.5L engine. Most have the hybrid LSD. These will always have fog lights, rear AC, power seats, and leather. Sunroof is also common on these. 16 inch wheels
03-06 models are based on the limited trim with a styling refresh done for the 05+. These will all have the same features as the Limited above, but use the 3.8L engine. There are no hybrid LSDs in these, but there is traction control which performs just as well. Traction control is confirmed by a disable button in the center console next to the seat warmers and rear AC control. I believe they added the 17 inch wheels in 05 as well.
Your stock options for limited drivelines are LSD without traction control (01-02) or traction control without LSD (03+). If it has both then the LSD was installed from an older vehicle. The traction control will be more effective than the LSD offroad. The LSD only affects the rear axle, but the traction control keeps torque flowing to the front axle as well.
The system feels like a LSD where one wheel will spin, but with more throttle, the other wheel begins to turn slowly to make forward progress. Just be slow and steady with throttle and you can impress anyone with how capable it is.
Here are some links showing the factory traction control in use.
https://www.youtube.com/watch?v=6vcfGK_9E6U
https://www.youtube.com/watch?v=fm1MGLUewuo
https://www.youtube.com/watch?v=3WPsT4p1lE8