Starfleet does homages? Doesn't sound all that likely.
The common design features between the two would appear to be the use of twin booms, the inclusion of "turbocharger caps" on top of those, and a bow cut in the saucer. The last is the least "homage"-like of the features, as it is typical of all the ships we first saw in ST:FC, and has for several decades been a fan favorite for making the neutrally round saucers look more menacing...
Twin booms are found in many fan or RPG designs, too, and indeed NX most closely resembles FASA's Loknar
class in configuration (although Loknar
had the forward ends of the booms underneath the saucer rather than atop). So the "turbochargers" (a feature borrowed from the twin-boom P-38 Lightning fighterplane of WWII for purely aesthetic reasons) are the one unique connection between the ENT and ST:FC/DS9 ships. A deliberate one in Paramount terms, of course, but do these fancy shapes perhaps also fill the same fictional function in NX and Akira
in in-universe terms?
As could be expected, those features were never assigned a clear on-screen role in either version. At one point, the Enterprise
spat phase beams out of them, FWIW...