I think you should've put this up as a poll. To answer your question though. It depends which prime. To me, Ali had two primes, the mid-60s and the mid-70s. I say Louis cannot overcome 70s Ali and gets hopelessly outpointed. But prime Louis could nail 60s Ali and stop him.
I've gone back and forth on this over the years. As I sit here now, I'd pick young Joe Louis coming up to beat young Cassius Clay. And I'd take Joe Louis as Champion to beat any version of Ali from 1973 on. And I'd pick old Joe Louis over old Ali (1976 on). But both at their absolute very best, I think Ali beats him quite cleanly. In other words, I think Joe was great sooner and Joe was great longer. But Ali was the greater of the two at their best, for what it's worth.
Joe Louis was a pro less than two years when top-rated contender and former heavyweight champion Max Schmeling defeated him. Two years into his pro career, Ali was still getting dropped by the likes of Sonny Banks. Joe Louis had knocked out four heavyweight champions ... including the reigning World Champ ... just three years into his pro career. Three years into Ali's pro career was 1963, and Ali was lucky to win a fight that year. Ali wasn't a great heavyweight in the early 1960s. Joe Louis was a great heavyweight about a year into his career.
For what it's worth, Eddie Futch actually boxed Joe Louis and Futch trained both Joe Frazier and Ken Norton to beat Ali. Futch actually used Joe Louis as an example for Norton to JAB when Ali JABBED and for Ken to keep his right hand in front of his chin (like Joe did) ... so Ali's jab hit Ken's glove and Ken's jab would hit Ali in the mouth. Norton's jab is the reason Ken was able to hang with Ali in all three fights. Imagine if Joe Louis was jabbing Ali instead of Norton. Also, Louis had a brutal, fast, short left hook. Everyone who dropped Ali (Banks, Cooper, Frazier) put him down with a left hook. And I'd argue Joe's left hook was better than theirs. That's why I think the only time I'd favor Ali over Joe was when Ali was a fully grown man (late 60s and early 70s) and still utilized a lot of movement. When he was younger he wasn't good enough, yet. When he was older, he laid on the ropes too much. He'd need his legs to save him from Joe's jabs, hooks and uppercuts.