How do some people rank Louis over Ali?

That reason would be that Ali was coming off a long spell of inactivity, and that his best wins were still ahead of him.

 

Sure, Ali wasn't seen as what he had been, but he was coming off stoppage wins over Quarry and Bonavena for chrissakes and was still the underdog. That says a lot about how highly rated Frazier was at the time. As he should be after beating aforementioned men himself plus Ellis and Chuvalo. He had been rated as the top fighter throughout Ali's absence. There is no one that Louis beat that had that kind of dominance over the rest of the division.

And his best wins were still ahead of him? Except Foreman, which one was better than Liston you mean?

 

Louis got out with a win in the first Godoy match and destroy him in the rematch. Ali may had amazing rematches vs say Fraizer or Norton, but he did not "Improve" as the other guy did make a good account of himself. Louis waltz in and lays em flat. What made Ali and Frazier, and their fights special was the back-and-forth action of their battles. How would the rival look had Godey got away with the win in the first match, Louis destroys him in the rematch, you think people would want a 3rd match?

 

I don't know who should be number 1, they are both great. And different. We will find valid arguments for each of them, and that's ok. But I won't agree with all of them, and I won't choose any of them.
The arguments for Ali are often not very good.
Speculations...
1. We cannot give him points on credit based on the fact that Ali had a 2-year break at the peak of his career. For what reason? and why over Louis? How to measure for whom this break was worse? if even this... Ali achieved his greatest successes after the break, Louis before. What would have happened if Ali had not had a break, what would he have done in the 68-69 season? ? defeated Thud Spencer?
2. Frazier ok.. When? Durham was cautious, probably 1969. Would Ali be better than Foley? I doubt it... he would start getting old already. He wouldn't be so hungry, he wouldn't strive for the top but defend it, he would be a well-fed champion. How do we know if the two-year break didn't help him regain his hunger and freshness? For me, Frazier is still the favorite, at most 50-50.
3. Ok, let's assume that Ali had beaten Frazier in 1968, 69 or 70. Would he have beaten ATG from a historical point of view? or rather someone like Tyrell Biggs? What would Frazier have without the victory over Ali?

Facts
Ali's CV is the best ever, absolutely. No HW can come close to him, no one has defeated so many outstanding opponents. But even a great CV can be overrated. Ali is Liston, Frazier, Foreman, Norton. But against Norton in 3 fights he was at best the same, I think a bit worse. It's hard to say with Frazier, I think the first fight was the best and most decisive. He caught Foreman and Liston at the perfect moment, perfect. These are great victories, but not as outstanding as they are portrayed