I will use them mostly for sporty road riding(not commuting) in twisty lanes and a few trackdays.
I’m between the Diablo Supercorsa BSB and the Corsa III. Does anyone have an experience with both
or either of the two? Frankly I’m mostly interested in the Supercorsas but I’m afraid it might be an
inferior choice to the Corsa III in terms of grip?
I went from BT014 to Corsa III on my ZX-6R, and I found they had more grip and compliance, and hence more stability whilst leant over. I find the Pirelli’s warm up quicker, too, and also superior in the wet. Not tried the Supercorsa, so cannot comment.
Here’s another consideration for you…I bought an RSV 1000 R earlier this year, and it has Metzler Rennsport fitted, which incidentally are manufactured in the same factory as Pirelli’s, I believe. They’re cheaper, and in my opinion, a better tyre, too. 
Metzeler Racetecs are the way forward…I’m obsessed, but never ridden on Corsa’s.
I’d say diablo corsa 3’s.
They will heat up quicker on the road and you have proper tread across the tyre, so if you caught in the rain it’s not so bad.
Grip wise on track, they offer loads. I used them at brands about 15 months ago, had a very good day, 53/54 second laps.
Still think Michelin make the best sport / sport touring tyre. 
Excellent tyre life, confident track day performance and great wet weather use (some guys were going knee down around Brands in the wet on Michs).
I’ve tried Bridgestone BT014, Pirelli Diablo and Supercorsa Pro in the past years of riding, but have found the best compromise of sport (track day and country lanes) and commuting tyre life (80 miles London to Essex a few times a week) in a combination of Michelin Pilot Power 2CT front and Pilot Road 2 on the rear on my GSX-R 1000.
Gotta agree with Afro there. Ive had the Pilot Powers fitted and they inspire a fair bit of confidence. Had Bridgestones on before and found they wernt as grippy hot or cold.
Just got to get the little stickers now
Always liked the Pirelli Diablo corsa 3. have them fitted to my 08 blade and love them. very stable and even good enough for a brisk pace on trackdays.