I've done both in May - my impression was that the gully is steeper.
This seems to be born out by my notes. According to my calcs, the gully starts above Iceberg around 12,600, and climbs 1,500 to the notch at 14,100. The chute begins above Trail camp at 12,050 to reach the crest at 13,400, or a climb of 1,350.
The one hiccup in the MWT is of course the 1.9 miles there and back (3.8). Depending on conditions, it can be fairly slow if there is a lot of climbing around/over ice/snow blocks.
If you have mountaineering skills (I don't, I was on a guided trip), then the MR might even be slightly easier from an endurance stand-point. The added miles on the MWT, and the sort of round about way to get there is pretty exhausting.
One item to note is if there is sufficient snow coverage, for those who are experienced & have been in the area before, you can literally walk a straight line down from Trail camp to Outpost by skirting the waterfall*. Then, cutting across Bighorn park down the creek outlet (usually an impossible bushwhack with sharp willows) will pop you out below LP lake.
One last note is it seems more people are using the old trail from behind the store, rather than taking the super long, switch backed equestrian route. It essentially puts you right at the main trail/N fork junction, so you can cut off around a mile or so on either route.
* Stay well towards the cliff side away from the waterfall. Also, avoid if the snow is melting and there are pockets forming. A girl fell and died there a few years ago by crashing through the melting ice cover over the precipice.
