I play with the generics more now that I'm older. I still use Story Characters for story missions (at least in Tactics) but I generally stick to generics. In later playthroughs, its been fun actually trying to tweak out story characters that have disadvantages (OMG I use Cloud but I actually don't use Finishing Touch Oh My! ) but overall, in the original Tactics, I enjoy twinking out all the characters and using different party set-ups.

In the TA series its different, I actually don't care for most of the Story Characters and very few have good advantages so I'm genuinely better off using my starting unit cause Story Characters rarely have strong advantages and tend to be underleveled. Since TA series has also gone out of its way to make grinding not an easy thing to do, its generally not worth the effort to use a sub par party for dozens of battles just so they can slowly catch up to the main party I use.