One of those dates is likely to be a transcription error, since I believe the Brides Index and the Grooms Index were not only kept separately by New York City's Municipal Archives, but were also keyed (transcribed) separately by the site's volunteers, and are only joined on Morse's site through the common certificate ID number. In order to find out which date is correct, I'm afraid you're going to have to request the original certificate and check it. Luckily, they're on microfilm at your local LDS Family History Library, free to use.
I would then follow up with an e-mail to the admins of the NYC marriage records site (not Morse, whose site just provides a more convenient interface for their database) and let them know to make a correction. I've found a few typos in names in their database over the years, and I do try to let them know of any errors so that it could be corrected for future researchers.