Cannonballs do not hold their value as well as Selmers and used prices are pretty good, even for the newer stone series horns.
I played a bunch of Cannonball and Selmer tenors and altos recently. The Cannonballs have a different bore that is bigger and has more emphasis on the low end. The response and tone of the Cannonball are actually quite good and comparable in quality to most other modern horns. The action is not nearly as good as any of the big four, however.
In contrast, the modern Selmers have some of the slickest ergos and action. Their refinement and balance makes it easy to play your fastest licks. The tone on the SIII is going to be brighter and more focused than with the Cannonball. The response is very good and balanced throughout the horn. The low end will not be as big and rich, but the high end is much better. Cannonballs get a little shin and shrill in the high end. Intonation on both horns should be good once you match the right mouthpiece.
If price is not a factor, the Selmer wins hands down, but with price a factor, Cannonball is not a bad choice. Cannonballs have gotten much much better over the last few years, but they still, in my opinion, have a ways to go.
Coincidentally, none of the modern pro horns I have played in the last year can hold a candle to my SDA tenor with the Barone neck on it. The only horns I've ever played that I even remotely considered better were Selmer Mark VIs.