Most likely a unified planetary government, but with individual states.
The world is getting smaller. The differences between the nations of Earth are getting less... differenty. Both the moon and Mars are already smaller physically, and will likely import the technology (and build new technology) to make their worlds small (global communication networks, fast travel, etc).
While humans will likely always exaggerate differences between groups to maintain a sense of individuality and to derive self-worth from those differences, small worlds will act more like differences within a nation rather than differences between nations. Here in the US we exaggerate the differences between the people of different states in the nation. While clearly the people of the Northwest are actually different (in a better way) than the rest of the country, we're all still Americans. We are actually quite similar. The savvy American abroad will claim to be Canadian, no matter what state they're from.
The cohesiveness of the Solar Government, or at least World Governments, will be increased by adopting a system somewhere between the United States and the European Union. Where we're all united under one small (intercontinental or intrasolar) federal government, but different states have control of their local areas.
Depending on how it's viewed, the answer to the question is then: both things will happen. Many individual states will divide the land united under one global (or solar) government.