I have fish both rivers. Both have there advantages. I prefer the LMF for the quality of water and and availability of different water types.
The Little Missouri is a great tailwater for the beginner fly fisher "person". When they stock that river it's like shooting fish in a barrow. You can't help but catch fish. If you bring your significant other and/or kids they can visit the Diamond mine and dig in the dirt while you enjoy the some great fly fishing. The access will be at the dam, Hinds Bluff, River Ridge, etc. Pay attention to raising water for you sure don't want to get stuck on the other side of the river when they are generating. Flies to take into consideration: Pink Winnie, Fox Tail Nymph, and several of Jeff Guerins patterns. Check out Jeff's web site for details about this river Arkansas Trout - Little Missouri Fly Fishing
The LMF is located in partly in the Beavers Bend State Park north of Broken Bow, OK. Stocking days can be the same as the Little Missouri but there are more areas to get away from the crowds in my opinion. Spillway creek has a number of great holes but you will run into more spin casters depending on the day of the week. Zone 2 below the Old Park Dam, Lost Creek and the Evening Hole does not allow bait and requires a barbless hook. There are other areas that have some great fishing if you are willing to put the effort to fish them. I would say the LMF has better access to all the waters mentioned. I consider it a more technical river compared to the Little Missouri in my opinion and fishes differently through out the year. Check out the LMF River Foundation
for some details as well as visit each of the fly shops that are in and outside the park.
Three Rivers Fly Shop - Broken Bow, Oklahoma
Beavers Bend Fly Shop
If I can be of help please let me know. Hopefully, I will see you on the one of the rivers soon.