Put simply, they’re just a completely different calibre of person. GHWB showed leadership from an early age, and earned his way to Yale on merit. He was also an accomplished businessman, who increased the family fortune through oil. He had real combat experience in WWII, which tempers most people’s foolish sensibilities about the utility of force, and he understood statesmanship and geopolitical realities.
The most important difference, in my mind, is that he knew that American leadership in the world was always best fulfilled by seeking to bolster and continue the legacy of the Atlantic Charter, advancing American national interests in international fora, and getting others to internalise American values. You remember - back when being multilateral minded was a bipartisan endeavour!
Bush never had anything like that kind of sophistication. He was not and isn’t a simpleton, like some pretend, but clearly he had little understanding of foreign policy coming into office. His tenure clearly shows how he was taken in by a neo-conservatives coterie who fed him a romantic bedtime story, which fit well with the brash and immature tone of Republican politics of time, and it clearly fed into his emotional need to reconcile his father’s loss of the election as a failure of will in the Gulf War.
As for how they governed, it’s also tied up with the fact that GHWB drew upon people with decent, credible views about diplomacy and statecraft, like Baker and Scowcroft. Bush too had some decent people, but they were marginalised for the most important decisions of his administration. He simply didn’t show the leadership to enable them to play an effective role in pushing back against the pugnacious crew Cheney, Rumsfeld, Wolfowitz, Bolton et al, who were waging an internal war against the State Department and Powell.