I run a Cobb tune Stg 1 agg. 93 oct. with Alpina B3 flash. I have felt no hesitation. In throttle response and lag it is no different then the stock setup as I have switched between them multiple times. Only difference is the Cobb has a lot more bite behind that bark.
Are you sure you have not selected linear throttle map. Because it is not as aggressive throttle setup as the standard throttle map. If so that might be the only reason you can feel the way you feel.
Also, I have had JB4 in past and I find Cobb better and smoother in its delivery.
nick named "BAD 3"
Cobb tune, RennArt catback non resonated exhaust, M-sport steering (racing alcantara & retrofit M3 paddle shifters.), Alpina B3 transmission flash, AFE powered sealed CAI, LED angels, E93 M3 Front Swaybar, 235/35/19x9 front & 275/30/19x9.5 rear. When in doubt...flat out