Tire size generally changes the drag curve, a shift up or down is generally a change in tire size, a change in tire shape can dramatically change the drag curve.
Here's some tunnel data comparing a few different tires on the 303 FC carbon clincher (internally coded x45FC). you see that the GP4000 23 and 25mm are similar curve shapes, only shifted in magnitude, while the Attack despite being narrower has a different curve shape due to the different tire shape...the Michelin PR3 measures over 24mm wide despite the 23mm printed on the casing, but the shape of the tire has changed everything, especially when you consider that the GP4000 25mm is still 1mm wider.
I've thrown a V shaped wheel in for good measure, you see that tires can have nearly as much affect on aero as rim shape. Ultimately, the most aero tires are all pretty close together for a given width, maybe running 10-15 grams different between them, while the less aero tires can really spoil the party. The PR4 performs better than the PR3 here, so I'm not trying to call out Michelin, this is just a good example of the effect of tire choice. Also, the Michelin 20mm measures more like 22.3mm, and performs between the Conti 23 and 25 curves below, so I'm purely using this to illustrate a point.

Kraig Willet has a great piece about this on his site, he even has data comparing Tangentes, Bontrager wing tires, Veloflex and some others... I recommend it. he also talks about comparing rolling resistance between the tires and offsetting the data relative to the aero charts...good stuff. http://www.biketechreview.com
Josh