It's great to see that you're thinking about who (or what) your client base should be, HereForDiscussion.

The idea that you don't need to say yes to every job that comes along is a difficult one for many independents. When you make the decision to limit your clients to this or that segment, you are letting everyone (clients, potential clients, and colleagues) know that you know who you are and what you do. You are controlling your business, rather than letting it control you.

As to which type of client is better, individuals or organizations, I believe there are advantages and disadvantages to both. For every organization that wants you to be an "active participant," there is probably one that wants you to be the "secret weapon" and another that sees you as nothing more than a particularly lively piece of office equipment. Getting paid can be more problematic--I've never had an individual inform me that their policy prohibits them from paying me for 60 days. (See also the campaign at the Freelancers Union regarding deadbeat clients). And it's true that your business clients will never be impressed by your private or individual clients, even if it's the most interesting project of your career. With individuals it can be more difficult to say "If you need me to do that too we need to revise the contract," so you have to be more vigilant about clients taking advantage of you.

I suspect it also depends on your personality. More introverted, or more autocratic, independents might not enjoy the group hugs required when working as an outsider in an organization.