There are a many threads that are auto vs manual debates. From my limited time here, they don't end well.
IMHO, based on limited experience with Z's but lots of reading here, neither is really
better than the other in the Z, they're just different. Performance is basically a wash, with a nod to the AT in terms of easy-to-launch consistency. Fuel economy is the same. Reliability is also probably a wash. Though with any manual, one can break stuff more easily due to human error (clutches burnt, forcing it into 1st at 80mph, etc).
If you don't want to be bothered to be required to shift, then get an automatic. Set it and forget it. When you need a specific gear, it has paddles. If you commute in the Z through daily heavy stop-and-go traffic, an automatic is probably the smart choice.
If you want a more "dynamic" relationship with your car, both
pleasure (absolute control, perfect heel-toe downshifts, the 'coolness' of being in the minority of Americans who know how to drive a manual) and
pain (how-do-I-launch-this-thing? stalling. why is the transmission so clunky? clutch-burnout-worry), then buy the manual.
One important note... If you buy a manual, the Sport package adds Synchro-Rev matching. When it's activated, the Z's throttle will automatically match the engine RPM to the correct transmission speed while you're shifting. Basically, it heel-toe's for you. It's a very cool feature, and it's the first (and currently only) car in the world that has this feature.
Good luck!