Originally Posted by omegaman
Is the radiation higher and more dangerous in space or on the planet?
As a rule of thumb, probably in space. However, the term radiation is a very broad term covering many different forms from different sources. Different types of radiation can require different types of shielding. Some forms at some levels, the dead outer layer of your skin is sufficient. Some require use of lead or some metal for protection. Some can actually be made worse by metal shielding (ie Bremsstrahlung effect)
thus a dense plastic is the preferred choice. Part of the reason we aren't directly bombarded by cosmic rays is because of the Earth's atmosphere. I think you can actually see a measurable increase in exposure to cosmic rays in people who fly at high altitudes regularly though I'd have to check on that. Another thing that has probably helped us here on Earth is our magnetosphere. I don't think Mars even has a magnetic field anymore. We aren't even sure if it ever had plate tectonic activity. While we do see what appear to be signs of it, overall, the planet is relatively featureless, suggesting that if it did have tectonics it ceased a long time ago and many of the signs probably have since been erased due to weathering over time. On top of that I believe Mars has less mass than Earth so less gravity and likely less atmosphere so there's potential of less protection planetside.
Sources of radiation are just as variable and are all around us. Lead 210 is one source of radiation that we are constantly exposed to here on Earth. It's naturally in the air and soil.