I have a couple of friends who do hair for their complete income. They both live very well. One has owned the shop and made very little money after overhead and other things. She thought it would be THE way to make it big and double her income but she found she was making about 2/3 of her income before. She went back to renting a booth and her income went way back up.
The good thing about renting a booth is that you do not have to pay for all the extras like electricity, sewer backups, water usage, etc...you only have to take care of your end of the agreement. The other good thing I can think of right off the bat is that you are not obligated to stay. You can leave and go to another salon at any time. You usually let your clients know you are moving and they follow if it in their ability. If they are limited to a certain area physically then they may not have a choice.... Being a friendly person and good at your job will make people like you and want to follow you where every you go.
The other option of working for an existing business has it's benefits too. You have a paycheck regardless of how many people walk in off the streets. One of my friends went to work at Penney's and made a lot of friends and when she left she took them all to the new place where she was renting a booth. You have everything supplied for you because they want to push their products. I like the idea of having a pretty predictable paycheck each payday for at least a while until you build a clientele that will follow you to a place where you just rent a booth.
So, all in all, I think renting the booth at least in the very beginning can be risky, if they don't come in you don't make any money. When working for a chain like in Walmart or Penney's you have a regular paycheck each week and it is pretty stable income-wise.
Renting a booth and having steady appointments is where the bigger money is though. The lady who went back to this could not make her caddy payment by owning the business and she loved that car. She went back to renting and had the new car paid off in less than 2 years. She lived in a nice home, had nice clothes and her kids had every known convenience.