MarketingProfs has a good, concise summary of the pros and cons of pay per click advertising (such as Google Adwords or Yahoo Sponsored Search) and organic search engine optimization. In an ideal world, you'd do both, but as they point out, sometimes budget constraints don't allow that.
Which should you use? The answer is, unsurprisingly, "It depends." One thing I'd add to the MarketingProfs piece: the tradeoffs can be very, very different for different organizations.
Scott Buresh, author of the piece, notes that the average search term price rose from $25 in October 2004 to $55 in December 2005. I don't doubt that, but average search term prices are not particularly meaningful when you're trying to make decisions for your organization. It's quite possible that the search terms for your marketing are under a dollar (I have clients with campaigns running now with those kinds of rates).
And if you're in such a niche market that the keywords have stayed cheap, chances are that you can do organic SEO rather inexpensively too - because the playing field is much less crowded.
Buresh also raises the issue of whether consumers find organic or PPC results more useful and trustworthy. Again, it depends.
If you're ready to spend money, the pay per click results are often much more useful than organic search results. Organic results are likely to include general articles, news stories, and blog entries while PPC results will include links to companies looking for your business, often with some kind of special offer (if they're doing their PPC program correctly).
Organic search is most useful when your customers are researching a future purchase. They're looking for information and advice, and they will probably look to organic results for reliable, non-vendor information. If you can provide something useful there, it's helpful. When they are ready to buy, a PPC ad that promises free support, a 10% discount, or some other enticing offer, that may be more powerful - the customer wants to complete the purchase, not read about it.
My suggested first step when you're trying to decide how to allocate resources between PPC and organic search - think through your customer's buying process, and start performing the searches that you expect them to do. This will give you a lot of insight into where you want your search results and ads to appear.
And if you seek out a marketer for advice, be ready to hear the only honest answer to this question: "It depends." But usually, both will be useful.