It's better in the long run... Adwords is a lot more expensive, but more effective you need traffic today!
SEO takes long time to work, Paid advertising start working right away but you have to keep paying. Like Patco says, SEO is better in long run if you do it right because the traffic you bring in will be free (or cheaper).
It is not that it is better than SEO it is just that if done both, it works well together. The thing is, adwords is not for every online businesses; you need to to invest money on it. Though it is a very good option if you can invest on it, and most of all if you know the work-around.
I woudnt compare those two, those two are 2 different traffic source so I will still use them separetly to get additional traffic source.
As stated above by @patco , SEO is better in the long run. SEO will help your pages/content climb the search results pages and help them stay at the top so that they will get more traffic by way of searches. AdWords is paid advertising that brings in traffic through the ads you are paying for. It won't work after you stop paying for the service. Basically, use AdWords if you need a site/page/etc to get traffic right now but also use SEO so that once you stop paying for advertising your traffic doesn't come to a screeching hault!
SEO has changed a lot since the earlier times. It is important to know what works for your brand for getting the right results. Also, SEO should be a combination of relevant backlinks, keyword variations and social media optimization.
I always give preference to SEO than Adwords. Because SEO helps a website to rank and also increase traffic and sales.
I agree with what some of the others have said. SEO is time consuming, but you definitely get better value for your money & time, because once you start to rank, your website traffic can only improve if you do not break Google's guidelines. With Adwords, if you don't know what you are doing, you will lose a lot of money. And even if you are doing the right thing, it's costly but you can get traffic today. If you have money to spend, do Adwords and SEO.