Here's my summary:
Their AP with haki scale to around the same level (relative to Admirals) which means that due to the fact that Rayleigh's haki scales higher, Sabo has better Base AP.
Rayleigh not only has better Haki potency, which would probably allow him to break Sabo's pipe, but he also has better haki usage with Buso Emission, which would help is defending against Sabo's flame-based attacks.
With this in mind Rayleigh would definitely hold the advantage at the beginning of the fight.
During his fight with Kizaru, Rayleigh showed that his stamina is not the best, only allowing him to fight for maybe around 10 minutes without getting tired and slowing down.
Because of this, if Rayleigh doesn't finish Sabo off before he gets tired, the advantage would completely switch over to Sabo.
Sabo is definitely capable enough to survive for long enough before Rayleigh slows down due to his training as a Revolutionary, where as a kid, he would fight against the likes of Kuma and Hack, who were much stronger than himself.
Sabo would be sure to catch on to Rayleigh's stamina draining, so I believe he'd take to the skies and slowly pressure him, shooting fire projectiles to either force Rayleigh to dodge or use more Haki to defend-- both of which would take even more stamina.
Rayleigh isn't stupid, so he would realize what Sabo is doing, but the sad part is that there's nothing he can really do about it.
If he were to jump in the air to attack Sabo, he'd be at a disadvantage, as Sabo can simply dodge or use his fire flight and stop Rayleigh, which would put him in a horrible position, in the air without an ability to fly against one of he most lethal fighting styles and ruthless characters in the series.
If Rayleigh stays on the ground, he'd eventually tire out and Sabo would swoop in and defeat him, but if he goes in the air, Sabo would use his Ryosoken and crush his skull.
I'm giving it to Sabo mid-high diff.