I converted a 1983 or so Centurion Lemans to a fixed gear bike. I really like the result and enjoy riding it. However there is something to be said to getting a modern (or old, but you need to know what you are getting) frame with a fit and geometry that works best for you. This Centurion technically fits me (its a 62cm frame, 57cm top tube, I'm 6'2") but it is not as nimble or smooth riding frame. I also ride a 2005 57cm Lemond Poprad (with a 58cm top tube) and it ride so much cushier, smoother and the handling is vastly more nimble.
I don't (yet) know the details of frame geometry effects and why there is such a difference between these bikes, but I do know that if I had a 'better' frame on my fixed gear bike I'd enjoy it even more.
Al