When correctly the two complement each other very well.
Your SEO efforts are to get organic listings. SEM helps you create a more effective and targeted advertising campaign that finds your website for words that do not rank you systematically.
Search engine land hits the nail on the head:
SEO: Earning traffic through unpaid or free listings
SEM: Buying Traffic Through Paid Search Lists
When working together, SEO and SEM are either stronger or work individually.
The important factor to remember is that both are only as good as the website that is being marketed.
If the website does not provide the quality that Google thinks users are looking for, then all your SEO and SEM efforts go without reason and will cause you massive amounts of frustration.
Start with a website that your users will like and then market and optimize from there.