While there are many things that will affect the costs of your procedure and care (the length of the procedure, your geographic area, the experience and reputation of the surgeon, the facility, the quality of anesthesia care), how long it has been since a procedure was introduced is not one of them.
Because your question implies this, I should also caution you strongly that just because a technique or technology is "NEW" or uses a "LASER", does NOT mean that it is safer, better, or more likely to achieve your goals than older, established techniques.
In this way, Medicine will always be different than shopping for a car... When buying a car, computer, or cell phone it is often safe to assume that new technology is better than old. Not necessarily so when thinking about your health and safety.
How to know the difference and be sure you're making the best decisions?
Don't worry about the details- spend your time and energy finding an ethical, experienced surgeon certified by The American Board of Plastic Surgery who can show you a history of great outcomes- then trust their recommendations.