I wasn't aware of the existence of the Akira before I saw the NX-01, so when I saw it, I didn't see a 24th century ship. The details that Drexler changed and added were very instrumental in the look of the ship and, in my mind, made it look like it was more primative than the Constitution. And I think In A Mirror Darkly portrays this well.
When the Defiant streaks over the 22nd century ships, it looks like some futuristic beauty next to them, with its seemless, white surface and confident lines. Everyone seems to think an older ship than the original series ships should be flat and white to show they are primative, but I think the sleekness and gleaming surfaces of the Constitution make the ship look futuristic. Maybe it's just a symptom of growing up in the iPod generation, but clean surfaces suggest advancement to me. Greebles suggest nitty-gritty mechanics, too primative to allow the incorporation of artistic forms.