I used own a manual performance cars like BMW M5, Quattro 20V Turbo etc etc. In recent years I've had automatics such as the Jaguar XKR, Volvo C70 and 996T and now the Supra.
I have to admit, with the Supra having the oldest gearbox, its actually holding its own against the newer cars and its a joy to use, very sharp and and precise, nice gear ratios, good reliability etc. I find auto's generally quicker and effortless on the roads. Had the 996T on a trackday and never even took it out of 'D'! I never even have to take any of my auto's out of 'D' even when pressing on some nice roads I enjoy the bike!
As others have said, if track days coupled with big power are your intention a manual would give you that few extra % on track.