filing dates are important because they often reflect the date of invention (or constructive reduction to practice). Your filing of a provisional patent application, assuming it accurately reflects the invention in your regular application, can be used as prior art to stop a later inventor (or filer in this case) from obtaining a patent. In summary, if you wrote a good provisional patent application, you're probably the winner. This rule was demonstrated in a court case about a year ago. An inventor, Giacomini, filed a patent application claiming a method of selectively storing sets of electronic data. Another inventor, Tran, filed a patent application after Giacomini for a similar invention. However, Tran’s application was based on a provisional patent application that accurately described the invention and was filed before Giacomini’s application. In that case, the Federal Circuit held that Tran as “first inventor,” could claim patent rights and use his patent application as prior art against Giacomini. In re Giacomini, 612 F.3d 1380 (Fed. Cir. 2010).
Would the outcome be any different under the America Invents Act? On March 16, 2013, the U.S. switches to a first-to-file system. Under that system, the first inventor to file gets the patent. So, the outcome would likely be the same as your provisional patent application would be considered the first filing. Again, that's assuming your provisional patent application accurately reflected the invention claimed in your regular application.