Adding to what has already been said here about recurving, Jeff at Advanced will also point out that you may want to "re-curve" just to restore the *original* spec to your dizzy.
Over time, the centrifugal weight springs inside your distributor can weaken (even break), and also the plates themselves wear and/or bind. So while you think you are getting x-advance at y-RPM, maybe you're getting more or less. When Advanced rebuilds a distributor, they will check the resulting advance curve against the original spec. to ensure that, in fact, these are working properly. Alternately, they can change springs and/or weights to get different advance characteristics.
There are some neat advantages come to mind regarding the 123 approach that dklawson notes. One of which is the ability to switch to different advance curves for different applications. I could see you wanting to switch to a more performance oriented advance curve on the days you take your TR to the track. And then switching back to something more tame for the street.