I've used both. They both only have one feature I use, that is they watch netlog file and keep a list of systems you've been to. Captain's log is more for explorers that want to keep track of systems they've been to. You can add stars and planet data into 'bookmarks', but it's all manual. I don't really like the look of it, it's fancier but not really easy on the eyes.
Like I was saying, EDDiscovery for all intents, satisfies the same use for me. Automatically tracks where you've been, with a minimalist interface.