He may have put greater pressure on the FBI and CIA to get Bin Laden and done more to prepare for an attack. If 9/11 still happens, he invades Afghanistan and focuses like a laser beam on getting Bin Laden. That said, the Iraq War unfortunately still happens. McCain advocated for war even earlier than Bush and he wanted Hussein gone. However, I feel that McCain would have liberated Iraq instead of occupying it as was the original plan. So the Iraqi army would still be intact and Iraq's basic social structures remain in place so the country is left relatively stable at least compared to OTL. He also would never have allowed the CIA to implement torture, for obvious reasons.
No Bush tax cuts, and we could see a cap-and-trade bill that Bush wanted before this was blocked by Cheney. I don't think McCain would have handled Katrina or the economic crisis very differently from Bush based on what I've read. In both cases he was reluctant to take action as it would have required high levels of federal spending and in the latter case interference in the economy. However he would show strong political leadership in both crises, whereas Bush looked like a deer in headlights much of the time.
IMO, it is better for McCain's legacy that he never became President. In OTL he is remembered for his wartime heroics and leadership as a US Senator. Had he been President during this time he would have taken the blame for Iraq, Katrina, and the Great Recession.