The last updated date is when the search engine was last configured (you can add your own sites to search). This isn't relevant, however.
In terms of how to interpret the results, that will always be an open question. However, I believe that certain point of search filters are not active on Google custom search.
My belief is that both result set use the same indexing criteria, so if your site ranks better in a CSE-based search, you are being re-ranked to a worse position when Google re-orders the results from the indexer for final display to the user. So, you don't have an indexing problem, you have a re-ranking one. This can help you isolate where to look for your issues.
This isn't a Panda/Penguin specific thing - it's always been the case that certain filters/penalties etc. are not active on CSE searches.
Incidentally, the accessible search used to have an option to display results seemed more "accessible" but I think Google forgot all about that :)