Geezer here with a stack of opinions as usual:
Most medieval crossbows feature more or less straight stocks. I have seen a very few that are bent downward to fit against the shoulder, but the vast majority are straight. Up till about 1600, they're generally quite narrow at the butt as well: perhaps 2 inches square at the largest. Long stocks, like siege bows (how long is long? I would say over 32 inches qualifies as long) might be rested atop the shoulder, like a modern military rocket launcher. Usually I rest my 31 inch target bow atop my collar-bone and against my trapezius-muscle (the triangular one that runs from neck to shoulder, just above the collar-bone) I find that a steady hold with a straight stock.
Shorter bows were definitely shot 'freehand' (according to period drawings, some rather long stocks were also shot freehand) So what's a 'shorter bow'? Well the Maximilian bows are about 30 inches long. Most of the short, fat-bodied German sporting bows are under 30 inches. I recently measured one in a private collection that is 27 inches and another that's 25 inches. With such bows, the shooter held the tail of the stock as if he was drawing an arrow to the cheek, just like a handbow. If you look at the short, fat Germanic bows, you will discover many feature a 'thumb-dimple' near the end of the stock. Clearly if that's your thumb-anchor point, you would be holding the stock near the tail and getting best leverage from the tickler
The advantage to shooting freehand lies in the facility for dropping the butt of the stock 'to the pap' in order to elevate for range.
Personally, I shoot a lot better from the top of the shoulder, but I spent my youth shooting target rifles from the shoulder. If I had trained to shoot freehand, perhaps I would find the position natural. So there's my two-bits. Geezer.