Admittedly, perhaps the Miranda could have been 10 - 20 years younger than the Constitution, but they aren't all that different.
That's true, it is strange that we see the Miranda in a combat role again after she was relegated to the role of a colony freighter in TNG - but that's Trek consistency for you.
It's interesting to note that the Mirandas in DS9 all had five digit NCC-registries, though, thus hinting at a much later construction/commissioning date. Probably the same idea of refits that kept the Excelsior-class in service for so many decades. The Constitution was refitted several times, too - it's just that she still did not prove to be as long-living as the other ships (we do see this in real life, too, though ... some designs are simply more successful than others).
When the shows technology is basically based on theoretical, superscience even technomagic anything can be possible. A DY-100 retrofitted with 25th century technomagic could hold its own against a Defiant class.