I'm lucky enough to be seeing both this week before they close. But if I could only see one I'd choose Finian's Rainbow.
The reason I'd choose Finian's is the fact that I'll probably never be able to see a professional production of the show in the near future again. While I'm sure this Ragtime is extra special I have the original production fresh in my mind and regional productions of this show pop up frequently.
"Broadway...I'll lick you yet!"