I would always prefer MGCP due to its ease of configuration, simplified Dial Plan, and lesser call-setup time. when would someone need H323 over MGCP. In other words, what can not be achieved via MGCP that would require administrators to use H323.
Here's a few things to consider off the top of my head:
MGCP does not support fractional PRI and BRI. There is a "bchannel maintenance" workaround for the PRI, but you're limited to five ciruits per cluster, and TAC doesn't support it as a production approach.
Drop & insert would be problematic for the same reasons.
SRST with MGCP is more painful to implement - you have to configure all the same pots dial-peers you would have had to configure for H323 in addition to the MGCP gateway configuration. And, you have to more carefully define your route-patterns to align with those dialpeers such that during fallback from MGCP and SRST modes, the user doesn't have to change behavior.
I've often heard call-setup time cited as a benefit of MGCP. I disagree with the lesser call set up time. I've worked with some extremely large clusters, that were purely H323, with and without Gatekeepers, and others that were MGCP only or a combination, and noticed often better setup times from the H323 clusters, particularly under heavy load.
I think, more often than not, poor setup times are a function of poor dialplan, not protocol.
No TFTP download issues.
Better scalability. Lower CCM CPU (no backhaul/q931) in addition to MGCP. Anonymous device support via gatekeeper strategies.
Better integration with non-mgcp, non-sccp devices such as netmeeting, CVP, any of myriad Fax servers, etc.
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