What would have happened, had the two fought under London Prize Ring rules? First, the downed boxer had half a minute to rest. Second, lack of protection of the fist (no gloves) would make Dempsey more cautious about his hitting to the head, as he could break his hands. Third, with wrestling allowed, weight advantage of Willard could come into play. In all the question is more like, would Dempsey make a good bareknuckle fighter, and did he have enough skills to beat the much bigger men under such rules?
Dempsey would definitely have needed to hold back on punches to the head though he would still have been able to employ a devastating body attack. Also Willard would have been able to take a knee whenever he was in trouble and get a 30 second rest. These factors would have made for a much longer fight and more methodical beatdown. A Willard win cannot be ruled out.
Willard's strengths (endurance, size, stamina, physical strength and durability) are likely to make him a great fighter under LPR rules. I'd still pick Dempsey, but if we're talking about a peak Willard who dethroned Johnson, who knows ?