Depends thoroughly on your definition of better.

If you're assuming that the lack of the United States would bring about peace, you are mistaken. First, there would be both an economic and military power vacuum that would send everything scrambling. China would have hands-down military supremacy, but would probably face vast economic set-backs. Countries in the Middle East and a handful of other countries would likely immediately declare war on their neighbors (North Korea-South Korea, India-Pakistan I'm looking at you.) This isn't to say that the US is the only thing keeping them from declaring war now, but rather that such a gigantic shake-up would leave the other powers capable of preventing such actions unable or unwilling to get involved.

The majority of the world's economies would enter severe recessions and even in developed nations I think you would find property rights severely threatened. You are basically describing a Nuclear Holocaust-type event, except rather than retaliatory missiles, those left remaining are going to struggle to assume the military power and economic strength once held by the US.

Within 100 years I think you would find either widespread socialism or a Sino-Indian Cold War.