Obama vs. Romney: who is better on space?

The quick answer to this is that 1) neither is particularly impressive when it comes to leadership in space, and 2) Congress approves budgets for NASA anyway so the president's view of space isn't the only thing that sets the agenda.

Item number 12 from this Nature article shows just how vague and unrealistic the two are when it comes to space policy. Obama's goal of sending humans to an asteroid is very doable; focusing on Mars for a flyby by the mid-2030s while the rest of the world is exploring the moon is not. His comment that the moon was not worth exploring because we've been there before was, to be honest, completely wrong. This post from the time it was said sums it up:

We have now added a new requirement for U.S. space missions – we must go to a place never before visited by humans...The new meaning of exploration contains within it the seeds of its own termination: after you’ve touched the surface, planted a flag, and collected some rocks or deployed an instrument, that destination is “done.”

Also add to that the fact that it is no longer 'we' that have been there, it is 'them' - another generation that does not have much time left on this Earth. We have never left LEO.

Now consider the things we have learned about the moon since we had a human presence there:

-- There is H2O and hydroxyl in the soil of the moon, which as far as we know can only be created by the solar wind. This process takes place on asteroids and other planets as well (Ceres, 23 Themis, etc.) and certainly takes place in other solar systems. We need to understand more about how this process works.
-- The most likely theory for the creation of the moon is that it was formed from us, as a result of an impact early on in the history of the Solar System. There are rocks on the moon that are a billion years older than any that can be found on Earth, so the only way to learn about our planet's earliest history is to be there.

Other things of use on the moon:

-- Seeing the long-term effects of 0.16g on the human body. We have only seen the effects of 1g and 0g. If 0.16g is fine for long-term colonization then Mars is a go, if not then we may be able to use results from long-term habitation to predict whether Mars is sufficient. The trip to Mars alone takes more than six months in zero g, making it very hard to tell whether any negative health effects later on were caused by the low gravity on the planet or the time spent in zero g on the way.
-- Building telescopes. Telescopes with no atmospheric interference and 14 days of night (as opposed to about 30 minutes at a time in orbit around the Earth), telescopes with complete radio silence, liquid telescopes, and so on.

Where Obama has been good on space has been investment in the private sector at a crucial period for the country. SpaceX has done wonders with their contract with NASA, and in a few more years we may see the first private sector human spaceflight. NASA's budget has also increased by a bit during his time in office, though the most recent budget has a slight decrease (0.3%).

Romney on space: extremely vague. Reading the article from Nature tells us nothing about his approach. On top of this the budget he has proposed is lacking in details, includes a large tax cut without specifics on where those funds will be made up, and extra military spending that the Pentagon has not asked for. On the whole the US budget will be healthier under a second Obama term, and his contributions to NASA, however small, make him the preferred candidate of the two when it comes to space. Voting Obama won't bring about a new golden era at NASA, but in the short term we'll see continued private sector cooperation and plans for a manned asteroid mission, which if nothing else is entirely new. Now we just need to find the right asteroid to explore.