In addition to time and money, there are a few other considerations that will dictate the best method of removal for your tattoo:
Laser seems to work best for folks with good immune systems, paler skin and a deep wallet. Different lasers are required for different colors, and seem to be most effective at removing tattoos with black, dark blue and dark orange colors.
Unfortunately, there isn't a laser that's adequate at removing turquoise, so dermabrasion might be a better option for colors that the laser doesn't respond well to. But, dermabrasion isn't recommended for facial tattoos because of the scarring, and it's also not as effective on older tattoos or deep tattoos, since it just deals with the top layers of skin.
Excision is a good choice for small tattoos in fatty areas that have looser skin. It's also more effective than laser and dermabrasion at removing deep tattoos. But if the color is super deep, it could require a skin graft.