Old Fixie: double fixed hub, two brakes, front canti, but at the rear a fairly useless Weinmann sidepull - I did hang onto it pretty hard a few times, but to probably only psychological effect, on the Dorset Coast, Elenith, though...TT'd on it with front brake only.
New Fixie: single fixed hub, two disc brakes. No problem with the rear brake and wheel position. [Genesis Day-One 853: track ends with screw adjusters, brake on the seatstay.]
But which set-up is best...hmmm?