Garand_Shooter has it right. X-rays, and the far more energetic gamma rays, are penetrative electromagnetic rays. Alpha and beta radiation are far less penetrative particles. Alpha particles, in fact, pretty much have to be inhaled or swallowed to be harmful; while beta particles (which are high speed electrons) can penetrate the body on their own.
After the initial burst of gamma radiation from the detonation, the lingering threat from that type of radiation hazard is relatively low. Fallout is radioactive for an awfully long time after the blast and is, IMO, the greater risk since if you are inside the blast radius you are vapor. In the NG, they taught us to dig in. Since the gamma radiation travels linearly, by digging in you allow it to pass over your head since it doesn't travel through the ground itself outward from ground zero. If you're exposed to the flash, you're exposed to the gamma radiation, in other words. That still leaves the particulate matter to deal with. That's where NBC suits and dosimeters and all that good cold-war era stuff come back into play.
I'd still worry more about biologic weapons, chemical weapons, and plain old high explosives.