Unless I'm mistaken, Active Drive II cannot be had on a compass anyways...
You can get active drive lo, but that is totally misleading, there is actually no lo-range, all it does is lock the transmission in 1st gear, although it does lock the front and rear axles... so, in reality it's 4hi with the trans locked in 1st gear.
That then means you are looking at the Cherokee, vs the Grand Cherokee...
In low range they are both locked front rear, and rely on brakes to transfer power side to side. The GC is way mor robust, but the 4wd is going to work the same... until one fails/breaks.
So, as mentioned above, it's going to come down to suspension travel, and, take a look at the suspension components, and you'll see the GC is certainly more heavy duty.
The real difference between ADII and QTII is going to be when operating in high range.
ADII is front drive, that, will react and send power to the rear when needed. If you watched the video above you see that while these fancy systems are reacting, applying brakes, and cutting engine rpm/power that momentum/flow is interrupted, or even stalled out.
QTII is full time AWD. Power split through the t-case is 48% front and 52% rear (normally), that in itself is a huge benefit, but on top of that the t-case is has a wet clutch that is electronically controlled and can send power front to rear without using the abs and cutting engine power.
My opinion, if odd roading is really important, and you want a Jeep wagon;
first choice, look at the '99-'04 GC, with quadra drive, solid axles for great flex, and, they actually rode very nice on road (gerotor limited slips front/rear and center, t-case, locked in Lo-range).
second choice would be '05-'10 GC with QDII, solid axle rear, independent front (electronically locking diff's front/rear and electronically controlled wet clutch t-case, locked in Lo-range).
- in '11 Jeep eliminated the front Ediff and went with an open unit relying on abs to send power from one side to the other... and also went 4wheel independent suspension.
Of course, as mentioned above, if off road is more important than on road, then, you're not going to top a Wrangler. The '13+ JKs are quite civilized, and the new JL's take it another step further.
Don't be afraid of the solid axles and the noted/reported inevitable death wobble... I put 260K miles on my solid axle XJ, never experienced DW, I had 160k miles on my solid axle WJ, never experience DW, I currently have 64k miles on my JK Rubi, again, no DW.
The DW is almost always a result of worn ball joints, and/or worn track bar/mount/attachment. Both of these are almost always a result of people adding lifts/bigger tires without addressing either item... and, this is usually uneducated consumers purchasing cheap lifts (marketed as a complete lift) that do not include all the bits to make them work "right".
One that note, my XJ was lifted with big tires, and my JK is lifted with big tires. To lift a rig "right" is not cheap... take the cheap road and you'll end up with a ill-handling, rough riding self-consuming nightmare.
If you are not loyal to Jeep, and you need to buy new rather than used, it's going to be hard to beat a 4Runner as an off road capable all around wagon... it's kind like a Wrangler Rubicon and a '05-'10 GC had a baby... it came out with body on frame, solid rear axle with a true locker, and just enough GC luxury/quietness to make it acceptable as an on road rig. Not as capable as a Wrangler, not as comfy as a GC... falls somewhere in the middle. biggest down fall compared to the Jeep wagons is no AWD for the 4runner...
