I shopped for and bought jeep Commander just this past fall and also pondered the issue of Quadra Drive II vs Quadra Trac II and can tell you these things --
1. A Commander with Quadra Trac II will, I believe, have a plaque on the center console below the shifter that says Quadra Drive II. If not, then the Commander has either Quadra Trac II (if a Limited) or Quadra Trac I (if a Limited or a Sport). There are other ways to tell from looking at the rear differential case, I believe -- look on this forum.
2. You can also use the VIN number to look on the Jeep website and get a build sheet. It will tell you all of the equipment and options.
3. Don't trust the dealer or a private seller as to the 4WD system. I found that they are usually ignorant.
4. As for the advantages and disadvantages of each system, look on this forum and on you tube, and there is a lot of commentary and opinions. The Quadra Drive II system is the better system, but I found it to be much harder to find a Commander with that system.
5. The Jeep Commander that I purchased has Quadra Trac II, the "lesser" system, because in the end I concluded that other factors such as price and condition were more important.
6. This I can tell you -- after driving my Commander for the past several months, both off roading and in deep snow and icy conditions, the Quadra Trac II system is indescribably better than the 4WD system on the 2000 Dodge Durango that the Commander replaced, both in capabilities and ease of use. And the Durango was pretty good (it has low range and a locking center differential, although open front and rear differentials).
7. This forum is the best source of information for Jeep Commanders,and the members are very helpful. You will find an answer on this forum to just about any question.
8. The Jeep Commander is a great vehicle, with an unmatched combination of size, comfort and off road capabilities, as well as price in the used car market.