It really doesn't matter which one you choose to integrate with the CUCM. CUE integrates with CUCM using a JTAPI application and CTI Quick buffer Encoding protocol. The CTI ports and CTI route points control configured in CUE control the voicemail and AA applications.
So with that being said, as for the protocol to use is really decided on what you want to configure. MGCP is typically easier to configure since it is all managed from CM. With H323 you will have to duplicate your dialplan on the gateway as well as CM. YOu can also setup MGCP with H323 Fallback enabling the router to take over the CUE communication in SRST mode.
Can you provide more detail into what is not working? Is it all calls? The most typical mistake that an individual makes is with the Calling Search Spaces that are associated CTI Route Point and CTI Ports. Make sure these are correct..
Are you getting this error “Installer User Interface Mode Not Supported. The installer cannot run in this UI mode. To specify the interface mode, use the -i command-line option, followed by the UI mode identifier. The value UI mode identifiers...
The below trick might come handy when you have to add a new node to a cluster but you don't have or is unsure of the security password for the publisher. This procedure has been around for ages.
1) Login into the CLI of the Publisher.