Latent Class and CCEA are different approaches for finding clusters. CCEA is a generic clustering tool that takes in data, i.e. utilities and importance scores or other survey, demographics, etc. data. It has a "cluster on clusters" approach to find stable groups. Latent Class works the other way in that it takes the raw choice data and start putting people together, estimating utilities for each group, then repeats. So, we wouldn't really expect them to come up with the exact same solutions, though we would expect them to be similar if indeed a true cluster exists in the respondents.
In theory Latent Class should do a better job, since it's clustering on the choice data itself, rather than taking a 2-stage approach of clustering on utility estimates. The exception might be for ACBC data. Latent Class is often strongly driven by the none utility and many people have high none utilities due to ACBC's ability to hone in on preferences, and it hasn't produced great results in our (limited) testing. Additionally, since our Latent Class software only takes in choice data, CCEA might be preferred if other demographic variables are to be used as part of the cluster data.