If Folley had a better chin, I may have picked him and while he was skilled, he wasn't that much more skilled where I think he could overcome Williams physical advantages. So I lean towards Williams. But won't rule out Folley.
Oh, c'mon. Even if Williams was picked to lose, which wouldn't be unreasonable, there is no way Folley could knock him that fast. Liston couldn't do it. Folley sure couldn't. I don't think there's any way Folley knocks out Williams.
There are many good things I can say about Folley. He was what you call a methodical fighter. His feet didn't move very quickly but he was very purposeful--always lining up his power hand with his opponents head and shuffling with slight lateral movement wherever his opponent went. He kept his left low to protect the body (I don't think he ever took a lot of punishment there) and kept the right high to protect against hooks, parry jabs, and launch his lazer like right. Folley was very accurate. I guess you could describe his overall game plan as "slow but steady". He did not overly exert himself and had some tricky feints with his left hand to make it hard to tell when he'd suddenly leap at you. When he did let his hands go he had respectable power. He dropped Cooper and even the iron chinned Bonavena. He also got Liston's respect and busted him up a few times. Folley also had a nice short hook that he used in combinations that usually ended with his Sunday punch right hand. He rarely went to the body, only occasionally throwing a lazy flicking jab. However, Folley's strengths also factored into his weaknesses. Due to his lack of body attack and overall reserved style, his opponents often still had plenty of energy even in the later rounds. Folley also sometimes failed to capitalize on knock downs and didn't have much of a killer instinct. He was a little too cautious at times and could risk losing rounds or allowing an opponent to mount a comeback. Lastly, he didn't have a particularly good chin and this is probably why he was more of a defensive sharp shooter. Williams has limited footage but what we do see is a very athletic and explosive slugger. His long arms, speed, and power enabled him to land very painful clubbing shots from all angles. He had a very Roy Jonesesque ability to rapid fire multiple hooks in a row. He dug into the body and knew how to go for the kill. He had surprisingly good stamina for a slugger and had decent enough ring generalship to win decisions. Williams weaknesses included a lack of commitment to the jab. He would have been a much better fighter had he used those long arms to snap it out and set up his bombs better. He also lacked defense and sometimes left his jaw open when throwing combinations or exchanging. Williams could take a punch but was sometimes too brave for his own good and attacked instead of covering up, backing off, or using his legs to recover. In a fight it would really depend on the early rounds. If Williams comes out explosive and aggressive from the 1st bell, Folley would have a hard time getting into his rhythm and pace. Folley was however, an excellent clincher and wouldn't allow Williams to simply bulldoze him. At some point Folley would start to time the aggressive Williams with those sharp right hands. The problem for Folley though is that he was a skilled but fairly predictable fighter. He didn't have a wide punch selection and rarely got out of 1st gear. The middle rounds would be intense and both men would hurt each other with their hooks and rights. I think a determined Williams with major swelling in his left eye and a bloody nose eventually forces a TKO in 8 rounds or wins a close decision if Folley goes into his shell to avoid punishment. Only way I see Folley pulling this off is in a 10 rounder where he isn't at the mercy of William's relentless onslaught and manages to tame him and time him with his frustrating methodical approach. But more often than not, I'd favor Williams 7/10.