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Primarily demodulator and perhaps the bandwidth. FM does not require that linearity be maintained as AM does. Removing AM by limiting in final I.F. stages helps simple FM demodulators that also respond to amplitude variation that would just add noise to FM demodulated signal.
The analog AM receiver needs an automatic gain control (AGC) circuit to handle the large RF input variation due to radio wave propagation. In FM receivers the limiter provides constant envelope signal at input of demodulator. FM signals require more RF bandwidth to enable same base band bandwidth. So difference is in the demodulator, filters (as RCinFLA also mentioned) and AM needs AGC. In digital AM (On-Off Keying), the AGC may not be necessary.
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