Quoting the immortal Sheldon Brown:
"Most people find expensive tubulars too expensive for recreational riding...but cheap tubulars are distinctly inferior to good clinchers, particularly in that they tend to be lumpy and crooked.
Comparing high-quality tubulars with clinchers, including the rims, tubes, etc, tubulars save about 50 grams per wheel...but your bike winds up heavier, because you really need to carry a complete spare tubular, as opposed to a tube and/or a patch kit. This doesn't apply if the team car is carrying spare wheels/bikes for you.
If you don't glue your tubulars on properly, they can roll off, causing you to crash. If you get a flat on the road, you can't glue your spare securely, since the glue needs to dry overnight; as a result, you have to ride very gingerly on your spare, taking it really easy on the curves and descents. If you get two flats on the same ride, you're screwed.
Some people believe that tubulars corner better in the rain...but I never go fast on wet roads anyway. If you flat in the rain with tubulars, your ride is over, because there's no way to make a wet tubular stick to a wet rim.
Tubulars are fairly immune to "snake-bite" rim cuts, and may offer slightly better "suspension" action than comparable clinchers. Their rolling resistance is actually worse than good clinchers in most cases, due to flex of the glued section"
I'll confess to have never ridden them myself, on account of my large frame - but they scare the bejesus out of me in any case. Glue for godsake? For a showcase/period correct/Track bike (period if its that old -clinchers have been around for decades) I'd fit Tubs, but for a bike to ride I'd go clincher any day of the week. Tubs get very expensive if road riding as well.