Main thing with these trucks, especially the older ones with higher mileage is gonna be your driveline type issues. Check the Transfer case, front and rear differentials, and especially the transmission thoroughly. These are the most common trouble points.
Also, there is not an 01 model Escalade. They skipped over the 01 model year and then introduced the 02 redesign in early 2001. The Yukon Denali did have a 2001 model in the GMT800 body.