I just had to chime in here, once I saw this thread.
I voted that Palin is stupider than Bush; but perhaps it might be better to say that she's got more arrogance than Bush. Bush, for all his (many) faults, seemed to at least sometimes acknowledge his weaknesses, and rely on others to provide guidance when needed.
Palin, by contrast, seems to be so absolutely convinced of her own abilities (and so blind to her numerous faults) that she commits the same mistakes over and over and over again. Being Bush's 'handler' was difficult; but being Palin's handler is hell (a fact well attested to by all those who've been in this position, and then left). As numerous comics have pointed out, she's every comedian's gift from god, because there's no need whatsoever to make up, distort, or exaggerate things she does/says in order to get a laugh. You can simply show her, unedited, and be guaranteed of guffaws (or head shakes of shocked disbelief) every time.
Perhaps tied in with this is the fact that while Bush apparently believed he was 'doing God's work', Palin's belief that she's doing God's work seems far, far stronger, and more extreme. Again, probably attributable more to pride and arrogance, than to stupidity.