Krayzie and SID (AID) aren't "the means of performing the exploit", they define the resulting softmod, and they are different in terms of the features they enable and the options they give you. In fact, Krayzie and (the later versions of) SID both use the same exploits (the gamesave exploit to get control of the Xbox in the first place when you install the softmod, and NDURE to give you control at every subsequent reboot). So, you are not misunderstanding this - how you do the softmod, and which installer package you use, and which options you select during installation, can have a huge impact on the stability and robustness of your softmod.
The short version is that Krayzie 1.1.1 is better for noobs because it gives you far fewer options and forces you to have shadow C and virtual eeprom protection (essential IMHO for a safe softmod that can't be bricked by a simple deletion of one file on the C partition). If you are worried that your softmod may be a bit flaky then replacing it is the best option. The easiest way is to grab HeXEn 0.99B11-22 (use Google, password is Heimdall01), burn to DVD-R, cold boot with it, and follow the instructions to update the softmod to Krayzie 1.1.1 or Kingroach NDURE 3.1 (HeXEn doesn't install SID at the moment).
This post has been edited by Heimdall: Yesterday, 10:28 AM