Depends on the mission role.
But the one thing we know about the Excelsior
is that she was supposed to be fast. The Constellation
couldn't be an "insurance" design for Starfleet's great experiment at fastness unless she were designed to be fast, too.
Personally, I would say that Constellation was developed first due to sharing the same technology as the Constitution and the Miranda.
But the point would be, at any timepoint X, any organization would have the option of using old technology or new technology. And most would choose to use both
, since new has a great probability of failing, even if old is known to have reached its limits for sure already.
The Soviet Union built the Slava
using old solutions in armament, electronics, propulsion and layout, quite simultaneously with the brand-new Kirov
- not because it was cheap to build ships "just in case", but because it was hugely expensive to do so. Had Kirov
failed, vast sums of money would have been spent on nothing, which would be massively worse than spending 2 x vast sums on at least something