Liberty is going to be the much better choice offroad. It has an actual low range transfer case, and a solid rear axle which will give you more suspension travel/articulation in the rear.
Also, if you plan on modifying it, there's much more for the Libby.
Patriot/Compass isn't really designed for offroad. You can do it, but a Libby is set up much better for it. It seems to me the Pat is in the lineup to compete with the likes of the CRV, Rav4, etc. Being a Jeep though, it DOES have to have some kind of offroad ability, so in that class of vehicle it's tops. But really no comparison to something with a solid rear and low range.
Keep in mind they're also different classes of vehicle, so it depends on what your main priorities are. The Pat is going to get better mileage and probably ride/drive better on the street, and the Libby is more trucklike but a solid offroader and maybe has more cargo room/towing ability.
And the Pat has more ground clearance on paper, but less in the real world. They measure ground clearance from the lowest point on the vehicle, which is normally the differentials. Being that the Pat is independant suspension front and rear, there's good clearance under the diffs. The Lib has a solid rear axle, so the differential hangs down lower. However, common sense driving negates any disadvantage from this.
For clearance you really want to look at how much there is under the rockers and transfer case, those are the important places. Picture it like this - the way clearance is measured on the specs you've seen, you could put a 6" lift on the Libby, and as long as you left the stock tires on it, the clearance measurement wouldn't change. Now in the real world, in that scenario, which one do you think would REALLY have the most useable clearance, despite the specs?
Oh, and are you looking to buy new or used? If used, also look at the Grand Cherokee, it's also very capable offroad.