I made the switch recently on my old Raleigh because I got a set of ksyrium SL's at a giveaway price. So I put those on my less vintage roadbike and did the hand me down thing with the Raleigh. At the time, it did need either a new rear wheel or an overhaul of the existing wheel, so switching them out was basically a no brainer.
So what are the advantages that I found? Pretty much just a cassette hub. For me though, that's a pretty big one since I had already converted it to 3x7 gears and I was having problems with bent axles. For you it may not be an issue.
Tires weren't that big a deal. The way I see it, a vintage bike should be somewhat cheap and it doesn't need to be a super high performance machine. For that role, I'm already content with the tires that are available in 27".