Beau Jack vs. Joe Brown
Quite a styles contrast. Jack was the typical, meaty swarmer with oodles of strength and stamina. Brown was the wispy, smooth boxer-puncher with all the moves.
Style wise, I think Jack has all the advantages. Brown, though a sharp hitter, was never the kind of fighter to take you out with a well placed punch, and especially not against Jack, who was still somehow conscious after the murderous Ike Williams unloaded more than twenty unanswered punches on him. Williams didn't just throw everything in the textbook, he threw everything that wasn't in the textbook including the book itself and every other book in the library, and Jack was still upright and moving at the end. It's nearly a fact - Brown could not knock out this particular foe.
Some things that may point to a Brown win are his victories over the gallant Dave Charnley. Charnley was an excellent fighter in the mould of Jack, and Brown beat him twice in his prime. Charnley was a lesser fighter than Jack, however, and didn't apply as much pressure - he was also a southpaw, so he was hardly a carbon copy anyway. Though Brown had an educated left hand, his best punch was easily the straight right (particularly as a follow-up to a darting jab), and fighting left-handed, Charnley was far more open to this punch than Jack was. Studying the tapes, Jack is visibly more protected on that left side than Charnley, whose main obstacle was always Brown's right hand.
You could say Joe Brown vaguely resembled Ike Williams in style and use that as an argument in his favour, but it wouldn't be right. Williams was stronger and rougher, and was a very heavy body puncher. One thing that swarmers don't like is their own body punches being used against them - Williams slowed down Jack using this method and set him up for the head shots later on. Brown wasn't usually inclined to throw many downstairs and lacked the firepower to make them work in his favour anyway.
Brown liked to clinch a lot and try to get away with fighting only as much as he had to, but this wouldn't work against Jack, whose strength limitlessly surpassed Brown's. Whenever Brown went to take time off, Jack would be digging his ribs and bruising him with his head and Brown would probably be wise to ease off the grappling after tasting this in the early rounds. Jack would then have the fight his way as Brown struggles to keep up with the pace and begins to wilt under the pounding.
Ultimately, however, I don't think the fighters' styles play a big part in the outcome of this bout - it's their mentalities. Jack was a fighter who would fight as long as his legs were under him, whereas Brown was largely a businessman who wouldn't fight unless the money was right. Even when in the ring for the right amount of money, it didn't take much for him to sit down if he knew he was getting paid anyway. Brown only cared about his legacy to a limited extent, and this would be his downfall.
Jack would obviously force the action and I can see Brown spearing him occasionally and perhaps marking up his face, but once Jack gets those fists cranking and builds up his momentum, he's going to become unstoppable. Brown was never the most durable of fighters and was susceptible on his left side where his hand was kept low - funnily enough, Jack's best punch was his right hook. Brown's jaw and Jack's fist would fit together like two pieces of a jigsaw.