I completely agree that clients respond to you differently when you're a real business instead of a freelancer, contractor, etc.
Once I started saying I owned a business and stopped saying I was a freelancer, I could immediately charge more and my referrals got better. I was no longer the "I know a guy that does development" person. I became the "I know a web company" referral and companies are expected to charge more than freelancers.
I agree with the value based pricing concept but I don't think it's _always_ effective for newer freelancers or larger projects.
For newer freelancers, it's important to be able to establish an hourly rate that meets your financial goals. For most, that would include a salary, expenses and then profit for your business. After you're receiving steady work at your base rate, you can start experimenting with daily billing, project based billing, increasing your hourly rate and so forth. But it takes time to get there.
For larger projects, there's inevitably scope creep and project based billing can be dangerous. I've been burned a number of times on large projects and now I put a "10% overage" clause in my estimates. If the time to completion is more than 10% over my estimate the project immediately jumps into hourly billing. It opens up a conversation very early on and sets an expectation that my work is not an open checkbook.
"Working with individuals or small businesses can be tough because they are usually highly constrained by budget and do not understand everything that goes in to what you do. They want freelancers because they can't afford full time people."
I've also found this to be very true.
When I'm evaluating clients I consider whether or not the person writing the check is using their own money. More mature clients often have a marketing director or employee that has a budget. With entrepreneurs and small businesses, you're often speaking to the owner and they tend to care more about how much something costs. It's just more difficult.