A developmental edit concentrates on major structural elements like plot and characterization. Basically, it's looking at the story as a whole and not worrying so much about presentation at the sentence and paragraph level.
A good critique group can provide this service as well, but feedback from an editor is often useful for three reasons:
1) The editor may hilight issues that polite critiquers would be unwilling to address. Critiquers are often hesitant to suggest major changes like combining two characters or shifting scenes around; it feels too much like rewriting the author's story.
2) If the editor's any good, then he/she will have more experience than the average critiquer, and (presumably) be better able to home in on core problems rather than obsessing about surface details.
3) The editor gets paid. This means that he or she will spend several days thinking about the book, reading back through key sections, and drafting a well-thought-out summary of strengths and weaknesses. You're unlikely to get equal service from a free critique exchange unless you're doing it with your mother or your best friend.
My advice regarding professional editing vs. critique groups? Definitely start with a critique group. When you've gained experience knowing which feedback to use and which to ignore, and when you're starting to feel that your career's reached a tipping point: that's the time to consider hiring an editor.
*Please note that I am not currently seeking new editing clients. However, there are handy lists of on Codex and Kindleboards for those who are interested in finding someone.