Airfield and carrier scramble rates depend on readiness

Can an airbase at the same alert level launch more aircraft faster than a carrier?

Sometimes, but not automatically; deck parking, catapults, multiple runways, aircraft type, wind, and alert posture determine the real launch rate.

There is no universal answer because alert state, aircraft type, deck parking, catapults, runway layout, and wind all matter. A prepared carrier can cycle deck-parked fighters rapidly across more than one launch position, while an airfield may have multiple runways and no need to turn into wind. The useful comparison is operational readiness under the actual conditions, rather than the theoretical maximum of either platform.