This is completely speculative, since 9/11 completely changed the purpose and tenor of his administration. I can point to several reason he would be perceived as more moderate, less divisive, and quite possibly more electable entering a second election cycle.
1. Foreign policy (the element at which he seemed most ignorant and downright stupid) would be a much less important matter. Prior to 9/11, he handled foreign policy in a pretty capable manner. His handling of the potential crisis with China over the US surveillance plane which collided with the Chinese fighter and force-landed was handled in a restrained and reasonable manner. He seriously intended to reset US relations with Mexico and promote a liberalized immigration policy. His administration funneled more money in foreign aid to Africa than any previous administration. He had a realistic policy regarding Russia and China - neither too accomodating not too preachy. Without 9/11, it is doubtful the necons surroundng him could have ever sold the American people and the "Coalition of the Willing" on the Iraq invasion - the single defining moment that destroyed his reputation for many Americans and most foreigners.
2. He appeared seriously interested in domestic issues, and two of his initiatives (the "No Child Left Behind" education act and immigration reform) reflected his "Compassionate Conservative" rhetoric. Without the distraction of two wars, there's no way of predicting how he'd have been judged.
3. Absent 9/11, there would have been no Gitmo, no "war on terror", none of the aggressive unlilateralism that so irritated Europeans. He probably would have been a stronger supporter of Israel than his father, but without US bombs falling all over Iraq and Afghanistan, hostility to the US in the Islamic wourld would be about the same as under Clinton or Bush I.
4. His religious attitudes and social/cultural policies would not have changed, but just be seen pretty much as standard Republican fare. No big deal.
5. Environmentalism and Climate Change? Yup, he'd deny climate change and continue attempts to reduce environmental regulations, but this would have been a relatively non-controversial stance for most Americans. A minor issue in the election.
Bottom line, I suspect in GW's first term he would be seen somewhat as a "do nothing" president, having acheived a few domestic sucesses and having not particularly screwed up either. He would not have the divisive issue of the Iraq war on his hands. If the ecomony goes south, his reelection might well depend not on what he does (since many people intellectually realize the Prez has little direct control), but if he can relate to he American people and who the Democrats nominate in 2004.