Depends on what you're reloading. Some rounds (like .45ACP) are such low pressure, you can reload any brass for them just fine again and again and again. Others you can't. Generally speaking, pistol brass (straight walled) can be reloaded more times than rifle. Some rifle rounds can only be reloaded 3-4 times; others more. It all depends.
Some brass manufacturers (for rifle) have softer or harder brass, regardless of caliber. Others will probably disagree with me, but since I don't do any match shooting with my rifle and toss the rifle brass after 4-5 firings even if it may look fine, such distinctions don't concern me.
What caliber are you referring to specifically?