Probably almost nothing on design, because they already had a pretty detailed CGI model of the Akira, so all they needed to do was tweak the image a little bit, change some dimensions, and delete a few decks from underneath the saucer. (The side views are slightly different, Akira has more desk under the saucer) If anything they had a jumping off point.
However, NX-01 could have flow in DS9/Voyager, and I wouldn't have thought it out of place at all, it would look good in the fleet shots. The Centur is older looking than NX01
Though I must say.. the Akira is such a sexy looking ship.
I wish they had shown more of the lesser-known classes though.. Saber, Steamrunner, Norway, and the Enterprise-J from Enterprise.