I'm not so sure I agree with Reliant being as old as you suggest, Crazy Eddie.
I could see the question about the Reliant, but the the Miranda class
itself is a bit younger than the Constellation class. They are close enough in registry to be concurrent, but then so are the Constitutions. We know that all three classes were in service together in the 2280s, and we have reason to believe the Mirandas were active in the 70s. Given how little we know about their design history, there is ZERO reason to suspect they weren't already in service together in the 60s as well, especially given Enterprise's previous history.
At the very least, in "The Cage" the Enterprise was considered one of "our new ships" per Mr. Tyler.
Apart from the obvious implication that Columbia was a pre-warp vessel (time warp vs. non-time warp), there's the fact that Tyler never calls Enterprise "new." He says
"And you won't believe how fast you can get back. Well the time barrier's been broken. Our new ships can--
Okay, I improvised the last part, but he starts talking about "our new ships" before Vina's hotness breaks his concentration.
Our new ships can WHAT? Travel faster than light? Travel faster than yours? Or maybe "Our new ships can get you back to Earth in just a couple of days!"