I have searched high and low for a direct head to head comparison between the WK2 GC vs LR4 on youtube and google and this is all I have found:
It certainly did not answer which does better in deep snow, or rough off road, or truly bad terrain. Tires can make a great deal of difference--the LR4 and the WK2 both come with street H/T tires or all season rubber. Changing out to good A/T tires can make all the difference. Deep snow----6"? 10"? 2 feet?" Fresh frozen, slush, wet "sierra cement", glazed ice, fluff Idaho/Montana powder (Eskimo Innuits have 20 words for snow beucase they can differentiate 20 types of snow.) Just like there are probably 10 major variants of mud from wet dirt and watery gravel to deep Mississippi mud or Alabama clay gumbo that can double as axel grease.
I believe that the LR4 is very similar to the GC in capabilities. Jeep designed the WK2 with a bullseye on the LR4/MB ML/Toureg in mind. I base this not on head to head comparisons, but searching and watching and reading videos or articles for each vehicle---and each vehicle performs similarly in similar conditions.
It's tough to make comparisons even in head to head runs. Driver skills are not the same, the terrain line differ from first vehicle to the second, running over a stretch of mud and dirt or snow compacts the terrain and can make it better or worse by churning and smoothing it down. The first driver may make mistakes the second driver may avoid and get better traction.
I would love to see a good full blown test with several of GCs competitors even with all the uncontrollable factors thrown in the mix and let's see who is the last man standing.