Honey also has a higher viscosity, lending more to mouthfeel and such, in a wine, than cane sugar does... But it also bring to the table additional flavors - usually wildflower notes, and not everyone thinks those notes belong with every fruit or style of wine
Then theres unfermentable sugars which lend a bit of residual sweetness, as well as the "health benefits" of honey
As for actually making the wine though, the only thing affected usually is the acidity, like has been pointed out
I wouldnt call them all advantages in every situation, but theres definitely differences between honey and sugar