You should be using both on your website. Things like SEO friendly urls, meta tags, incoming links are all SEO things you can do which have no impact on SMO...However, you should also have share buttons on all blog posts, FB comments emended if you allow comments on posts, a link to your FB/Twitter somewhere on the site..These are all SMO things you can do which have no impact on SEO.
Implement and use both on your website.. It's a must at this day in age!
I don't think you can separate the two. Search Engine Optimization is an important part of Search Engine Marketing. If you want to do the marketing part right, you'll start with SEO and make sure you follow through with SEM.
SEO and SMO both are equally important for any website's promotion. SMO gives a much larger audience for your business, but SEO works as the foundation stone which keeps your webpages updated and help in gaining better search engine rankings. We cannot ignore any one of them.
I think this should not be either or situation. You can see that both are meant to have some value from the ranking and reputation point of view. There are some of the time when the SEO alone can do the work. But focusing more on the social media definitely helps a lot. It takes time for both strategies to work though.