My guess is that either a) Billy boxes circles around him or b) Max connects and the fight is over, the probability of a being slightly higher than b.
One of the ways Billy originally made his name as a young prodigy was in a sparring session with the fatherly Baer, who was clowning a bit, taking it easy, and leaving himself country wide open. Conn loaded up and slugged him, drawing blood from Maxie's mouth. The Larruper stifled a curse, then tried to tear Billy's head off, but only succeeded in whiffing air after a ducking and dodging Conn. After time was called, Max smiled and good naturedly asked Billy to never put him in a position of looking that foolish in competition. (I'd imagine Baer was having flashbacks to Loughran.) Both would have known in a competitive match that it would be Max by knockout, or Billy by decision. I think Conn succeeds in avoiding him, being much the faster. He tried to take out a weight weakened Louis after staggering him, an idea he wouldn't contemplate for an instant against the bigger, harder punching and iron jawed Maxie. For this one, he wouldn't be a "thick" Irishman, but box sensibly and with great respect for Baer's power.
Every fight I've seen of Billy Conn he does his fair share of standing and trading or fighting on the inside. He was not a stick-&-move kind of guy. He did a bit of that against Louis but nowhere near enough. If this was a 15-rounder I think Baer would knock him out. Conn does well for a while but sooner or later gets overpowered by the bigger man.
He was capable to do both things.....I would say he was really great when on the inside.....but he could move and fight with his jab against a slow guy like Baer... if Conn is at his best and if he was well focused.....
I'd give Conn more credit for having sense than those who think he'd stop and stand and trade with Baer. I think he made that monumental mistake against Louis, but if he was so compulsive about trading, he'd have lost more fights in his career than he actually did. i think he'd respect Baer's powerful right and iron chin, and would take a leaf from Tommy Loughrans's and Braddocks win's over Baer and would have put on a real jabbing/moving/boxing clinic with Maxie and would have snared a decisive points victory.
The second Baer lands a good shot with either hand it's over. Baer could go the full 15 in his prime no problem. There's just no way Conn can go the full 15 without getting tagged. No way, no how.
The only light heavy i think could beat Baer would be Tunney because he knew how to fight of the back foot, keep good range and could back peddle hard, also he seems very durable but i don't know the extent of how proven his chin is. Even then i wouldn't exactly favour him...
Probably just as interesting that a Red Cobra has Sammy Angott in his avatar, now that I think about it.
I think Conn and Tunney clearly had more proven chins and far superior power to Loughran, although Tommy was a better boxer than either. Max Baer-Loughran II would've been interesting after Maxie received generous tips from both Dempsey and Tommy himself. I think Max's lack of hand speed always could have plagued him against LHW cuties who could move and take a shot. Farr took the first one over him largely on the strength of his jab, and the Larruper never crossed paths with Bob Pastor, which could have been a revealing encounter. But sub 200 pounders were certainly able to compete with him, and even win on occasion. I think Greb would have driven him nuts with the kind of speed and stamina Harry possessed. Max would have felt like he was being swarmed by black flies or locusts.