Web design and SEO should be symbiotic. After all, there is no point having a wonderful looking site if nobody can find it. This site, by contrast, has no design whatsoever. It can however be found.
Am I saying that SEO is more important than Web design? Not really. A good web designer will incorporate basic SEO into a site as they build it. Not having any design (wordpress default style) is not a good thing though. While the content on this site is good (or at least I try to make it good) a lack of design leads to me losing traffic. This shows up as my bounce rate which is high enough for me to be embarrassed to print it here.
Of course there are other factors. My writing style could do with an overhaul most of the time for starters. There is no getting away from the fact though, that the first impression of this site is that it is unprofessional. Nothing could be further from the truth in reality, but it is not a warm, inviting, friendly site.
This is not because I am not a warm, friendly or inviting type of person, it is purely down to how the site looks.
SEO will get a site noticed. It will get visitors. Keeping those visitors requires a little extra though. Both Web design and SEO are extremely important. The reason this site does not have any design is because I wanted to see the effects of bad design. The wordpress theme is not necessarily bad, but it gives an impression of little effort. It also firmly aligns itself with spam blogs (splogs) by not altering the theme. This is because the majority of splogs do not bother altering the theme either.
When I change the theme I expect to see a change in my stats. That will not be for a while yet though. I am not finished collecting data on the current setup.
For me, SEO is more important than design, but it is a mistake to ignore web design. Equally it is a mistake to ignore SEO.
Of course to really market your web site online, holistic SEO is the way to go. Do not look at the web in terms of SEO vs Design, Adwords Vs SEO or Social Media Vs Adwords. Look at it in terms of a marketing medium and bring in everything. There is no more cost effective medium for marketing. Use it to its full potential to sell your business.