I have never seen or worn an Ohm, however, I used a GG Mariposa Plus on my trek last year. The Mariposa Plus has 2,800 cubic inches in the main compartment and including the outside pockets it has a total of 3,600 cu. My base weight before food and water was 12 lbs. which included any group gear I had, such as a 4 qt. pot, stove and a bear bag.
Your pack choice will alsol depend upon how much troop gear you take. We all went lightweight and besides the our own tarp, 2 pots, bear bags, ropes and the never used Philmont issued Frisbee, we were pretty much hiking like we usually do.
To me, food and water are the main issues. Food at Philmont is heavy and more importantly, BULKY. Nonetheless, even with a 4 day resupply I never filled my pack main compartment to the top. If I were to buy a new pack for Philmont I would buy a Gossamer Gear Gorilla just because it is a paired down version of what I already have.I think I would still have room in my pack. As far as using an Ohm you just need to make sure your base weight is low enough so that you can handle the heavy resupply days.
It also depends upon how bulky your items such as tent, sleeping bag and pad are. If they are real bulky you may run out of room. I used a Montbell SS#5, Torsolite (which does not go inside the pack), GG The One and a Polycro groundsheet. Few, clothes, toiletries, etc.
I never ran out of space and was always comfortable.