Well, I'm an old min/maxer from AD&D days. It's a hard habit to break. However, I try not to sacrifice fun for the sake of having the best stats.
My engineer flies the Excelsior Refit first and formost because it's the tank that I'm fondest of. Before I played STO, the home ship of my Star Trek fanclub was the Excelsior Refit. I became an authority on it while serving as initially the Chief Tactical Officer, then the Chief of Operation and lastly the Chief Science Officer. After extensive study of the ship, I determined that if there is any safe place in space it would be aboard an Excelsior Refit.
Returning back to the subject. I keep some but not all of my character's previous ships. Every once in a while, I get in one and fly around. As Asimov implied, PvE don't require the latest and greatest ship to win. So have a little fun while you're going about your missions. Get in your favorite ship and show Kirk how it's done.