I have the iOS and Mac versions of MacJournal, and the iOS version of Day One. I got into MacJournal before there was a Mac version of Day One, and have used it quite heavily for a number of years... but I was using Day One on iOS before there was a version of MacJournal for iOS.
My impression was that Day One for iOS had a nicer interface, but that MacJournal overall was a bit more powerful.
Given your question, though, I took a look at how Day One has developed on MacOS since the last time I saw it. Day One version 2 has been out for almost a year now, and it looks like they've added some impressive features that I'd actually really like to see in MacJournal. So now my impression has changed a bit:
For pure journaling, Day One looks like it might be the nicer option. If you're looking for an application that can be a bit more versatile (blogging platform, general information management), MacJournal might still be superior... but I'd need to use Day One a bit to get a feel for that. Pity they don't have a demo version; I'll have to examine the screenshots a bit more, I might just switch over, myself.
Edit: Looking into the features a bit more, it looks like Day One may not support video import in journal entries. I actually save a fair bit of video clips (whether home videos or YouTube rips) into my journal. So MacJournal remains a more powerful option, but if you don't think you'd ever want video in your journal, Day One is still a strong-looking candidate.