If you want a handheld whose original RPGs are better than its remakes, going to the 3DS would be a horrible idea.

I always recommend Valkyria Chronicles 2. It is somewhat story-battle but not in the linear way you might be dreading, as you unlock side missions and character interactions depending on the characters you use in battle and there's always a variety of things to see and do, instead of forcing you down one path. The gameplay is also just so new and refreshing, there's plenty to fall in love with. It's the evolution of the SRPG formula in case you're unfamiliar with the series.

You might want to try some top 25 lists and such on Google. I've heard great things about Ys Seven, Legend of Heroes: Trails in the Sky, Jeanne D'Arc, Half Minute Hero and Gungnir. I honestly didn't play a lot though because the PSP had so many great games outside of the RPG genre.