The biggest difference between the BK Rush and the BK3 is mainly the Revo break shaft. The BK Rush's carbon fiber shaft transfers energy a lot better than wood as it has a higher coefficient of restitution (COR). In simple terms, carbon fiber is more elastic than wood, which in turn gives more speed to the cue ball. The carbon fiber is also a stronger and more durable material that will not ding, dent, or warp, and will therefore last longer.
On the front-end side the tip materials are also different. The BK3 features a phenolic tip and the BK Rush a hybrid leather tip impregnated with phenolic resin. The BK Rush Hybrid tip is a bit softer and allows for better cue ball control than the phenolic tip. Since BK Rush transfers more energy thanks to its carbon fiber construction, the hybrid break tip giving more control provides the best balance of power and cue ball control.
Other than that, the BK Rush and BK3 butts have similar specifications as both have a 4-piece spliced butt construction and they are both break balanced (rear balanced with a standard weight of 18 oz).
You can find them here:
For the United States: https://www.predatorcues.com/usa/products/break-jump-cues/break-cues.html
For other countries: https://www.predatorcues.com/int/products/break-jump-cues/break-cues.html