First off, go back to the dealer, tell them that their price is too high, and unless they can be more reasonable then you will be going independent. That might just encourage them to come down a fair bit. However, you do need to know EXACTLY what the dealer is quoting to do, compared to the independent. The dealer price might include a brake fluid change, coolant change, fuel filter change, etc, etc.

If they aren't willing to move on price, and if the work being done is similar, then I'd personally go independent. It's not as if the car is still under warranty.

While you're at it, go have a look on here regarding the oil filter strainer (I think it's called that), which Mazda dealers never change, but if it blocks up will write off your engine. If one of those is on your car, ask the independent for a price to change that too