The only thing about the Constitutions being too small or ancient is that they seem to be a prestigious posting (DSC quote), and Kirk talks with considerable pride about how there are only 12 like her in the fleet (TOS quote), sort of implying they are a notable class (he may have been referring to only his subclass). Additionally, I seem to remember a quote from either TNG, DS9 or VOY about how Kirk discovered more planets than anyone up to that time. Considering how big Starfleet likely is, it suggests they were in some way very efficient explorer ships.
I don't generally like to mention Axanar because of the controversy, but I quite like the order of Klingon design history they came up with. They seem to place the Raptor-class as an early battlecruiser (perhaps relegated to a scout later in it's long lifespan). They place John Eaves unused D4 class next. Then the D5 class from Enterprise. Then a new D6 class design that looks nicely transitory, and slightly resembles the Kelvin battlecruiser. Then the D7. Say, if you wanted to also fit the Kelvin battlecruiser in, it could be a variant of the D6 or D7, or maybe a D8. Then again, maybe the D-classifications are Vulcan designations and actually have no relation to the age of a design, and are instead what order the Vulcans encountered Klingon designs in (like M-class from the Vulcan word Minshara). I have no clue in hell how the Klingon fleet of Discovery would fit into this pretty good design history, maybe privately-built non-military ships. Maybe something like this:
Generation 3
Generation 4
Generation 5
Generation 6
Generation 7
Generation 8
Civilian design, owned by a private Great House, from Generation 8?
In terms of where these ships line up with the Starfleet ones above, I would guess the D7, which we (unfortunately) saw on screen in Enterprise was a contemporary to the NX, i.e. generation 1 of Starfleet, but was refit repeatedly (maybe a half-dozen times between 2156 and the Dominion War) with new technology, being an especially robust and adaptable space frame. That would make the D5 rougly a contemporary of the Daedalus class or something, but of course, as in real life, technology might progress at different speeds depending on the political and scientific environment; I imagine Romulan and Klingon starship research went much faster after competition with the scientifically innovative Federation, but may have been stagnant before that, and that the D7 was much more advanced than the NX.
But in terms of fan films, I rather mention the far less controversial Pacific 201, by EC Henry, who does some of the best Star Trek and Star Wars analysis on YouTube. I agree with his philosophy of making the first ships of the Federation look really really grounded in current science, they look much more like a NASA spacecraft, except in 22nd century form. The USS Pacific with it's smooth white hull, greeblies and visible antennae looks great I think. Dunno how the film will turn out, but the design was really well thought out and looks ship-like with a conning tower. Pictured here with a refit NX-class and Daedalus-class, also given smooth hulls in refit.
. And lucky how the ship is more or less designed to be redone bit by bit, component by component.
