The issue is that kelp/seaweed comes from the sea, so you need to be careful to check that your kelp is not from polluted areas. I personally wouldn't want to ingest any from Japan for example. The supplemented form of iodine is mined in a number of places, so in a sense it is just as natural as the kelp, it is just sourced differently.
There is a similar example with salt. The argument is that sea salt is at risk of contamination from pollutants in the oceans, where as the rock salt mined from mountain ranges in Pakistan is not from polluted sources. Unfortunately I've only seen this debated on websites that sell either salt so I can't say who is correct on this.
Here's an article on the issue of arsenic found in kelp samples: High Arsenic Levels Found In Herbal Kelp Supplements
I think the amounts are probably quite small, so if you want low doses of iodine then kelp is probably the way to go. Over in the iodine thread and on the iodine yahoo group some people are taking very large doses of iodine and that would require extremely large amounts of kelp. In that case I would supplement.
So long as you are not using therapeutic doses of iodine, stick with the kelp, but don't be overly concerned about supplementing. Just because something comes out of the sea, doesn't make it any healthier.