My thoughts:
1) She had a small air group.
2) Due to power for her catapults being limited she could only launch a strike of less than 30 planes before having to wait a significant time to get steam pressure up again.
3) The catapults were complicated and represented a number of points where failure or damage could severely hamper operations. The catapults also severely limited rolling take offs.

As far as air ops she would have been inferior to a US CVL although faster and tougher (at least in regards to sinking perhaps more vulnerable as far as air ops goes). Overall as designed I don't think she would have been very effective. There's been a long thread on her over on the axis history forum where they've surfaced a lot of interesting details.