Whether it's April's Enterprise or not, it seems like that starship has subtle differences, like better proportioned nacelles for one. The freakishly large Hod Rod ones are pretty much a new development. So not much of a surprise to me, finding an older generation of ship, has better lines I'd approve of.
I don't think we're thinking like movie writer/producers. Which I imagine generally involves thinking "Hey, wouldn't it be COOL if...?" Because films like this basically boil down to one or two set pieces an audience will look back on and remember.
Well. Hey wouldn't it be cool if we could have two Enterprises fight each other?