Depends on what you mean by "field processing". For me, medium sized game equates to whitetail deer size and I just did the field chores (often with a folder for years), dragged the deer out to my vehicle and hauled to a butcher to finish "processing" into usable sized chunks of meat.
If I were doing all the processing in the field, I would do the same thing, except drag the animal to camp and begin the skinning and processing.... small knife for skinning and larger for cutting up meat.
I don't hunt much anymore, but I went with a small fixed blade for general hunting and field chores with a traditional folder backup such as a GEC #42 knife. For years, I simply carried a normal size jack knife in the woods, used it, and cleaned it. I eventually moved to a Schrade 250T (Buck 110 size) which I preferred for whitetail deer. Then came the fixed blade.....