Job security is/is not a myth. It depends on the company. However what it all comes down to is when the money runs out, you are out. If you are a mission-critical contractor or a mission-critical employee you have more job security than a non-mission-critical contractor/employee. If people feel that you truly overcharge to hell and your services are not worth it, there you go, no job security.
What is better about employee? You have a regular paycheck. Economy is shitty? You still get it, or get fired. Economy is booming? Still get it. Didn't make a sale this month? Still get it. Contractor is not so consistent.