Yes! I just beat this game two days and I absolutely loved it. I came from Persona 4 as well and although there are lots of gameplay improvements in P4, everything else is just as good (if not better in some cases). Stick through the minor gameplay annoyances and slow-starting story, and I'm sure you'll enjoy the hell out of it.
You basically got it right. A commentator might say "he went in the lab and developed some new tech", which is just a fancy way of saying that he went in to training mode and came up with a new technique/combo..