If Ace had survived and vowed to become Pirate King to honor White Beard's memory, how much of a threat to Luffy's ambitions to become Pirate King would he be by now? People like Kidd are jokes compared to Ace. Ace had the blood, the backstory, the power. The effortless charisma. The ridiculously strong allies like Marco and Yamato. He's a true contender and the narrative takes him very seriously.
I love this question, especially everything that attributes to the possibility of keeping Ace present in the story.
First and foremost, if Ace were to start competing to be Pirate King, he wouldn't do it for the title. Rather, as you said, he would have to honor Whitebeard's memory and perhaps assume the position of "The Strongest Man in the World." In addition to all of this, his main goal will always be to defeat Teach.
Now, how does his relationship with Luffy fit into this? Ace and Luffy would go all out against each other, but not to the point of killing the other. Each has their own reasons for this: Luffy wants to prove his strength to Ace, and Ace would want to constantly verify that Luffy has the strength to continue on this path. Canonically, Ace isn't interested in being Pirate King, but making a name for himself requires facing those vying for the title, so it's not a bad idea to visualize two or three fights between Luffy and Ace at different points:
-The first: Ace has to leave Rukushina/Amazon Lily after seeing that Luffy is stable. Luffy wants to accompany him or doesn't want Ace to leave. But this results in Ace having to show him the power differences he will encounter in the New World.
-The second: In the Wano arc, Ace would be a central figure. As soon as he heard from the news and through Marco and Nekomamushi what Luffy was planning to do, he immediately left with Whitebeard's fleet for Wano. The confrontation would be brief, but it would be enough for Ace to notice that Luffy has become stronger, however, he and the other more experienced pirates know that it's not enough to face Kaido. Whitebeard's fleet battles Big Mom's ship at Wano Waterfall, while on Onigashima Ace, Izou, and Marco are constantly at the center of the battle, Ace can face Big Mom (either alone or with Torao and Kid).
-The third: At some point, the last Poneglyph will be the epicenter of the ultimate battle between the pirates of this era, so this would be the moment where both give their all against each other.
Although of course, there are many variants, especially the order in which each character falls between Luffy and Ace's objectives, but I definitely think Ace would have been a constant wake-up call for Luffy, and definetly the story would be different (Dressrosa, for Example)











