I also really didn't like Courtroom Revolutionnairé 2016 at first, but I think it's grown on me.
This is the first I've heard of this, and I kind of don't really like it too... It's pretty much just Athena's first Objection theme remixed so that its missing everything I liked about it. I mean, I was skeptical about the original at first because it didn't really sound like an Objection theme, but it really started to grow on me because it was so unique, and it quickly became one of my favourites.
Honestly, Dual Destinies just had great music overall. Objection! 2004 used to be my favourite Objection theme, so the fact that Objection! 2013 is basically just that without mandarin quality made it my new favourite. And as I already mentioned, Courtroom Revolutionnaire 2013 is a close second.
My favourite case would have to be 3-5, with 2-4 as a very close second. 3-5 is pretty much the perfect climax, filled with tons of great moments, and it's perfectly paced so that every time you're starting to come down off of an exciting reveal another one comes by and gets you excited again. 2-4 had lots of great character development, and if you ask me probably does the best job of defining what the series is about. It's also incredibly painful in the best kind of way. The first time I played it I genuinely couldn't figure out how there could be a happy ending, and I wish I could relive that feeling of dread.
One of my favourite cases has to be 5-3.
I really really like 5-3 too. It was definitely my favourite case in Dual Destinies. DD is actually the only game in the series where I preferred the filler cases to the actual plot cases, due to a combination of the filler being surprisingly good and the actual plot having some issues that really bugged me.
Favourite character would probably be some kind of four-way tie between Gumshoe, Franziska, Pearl, and Athena. It's really hard to choose.