NFL would have filed first in NY no matter what. They had the papers all drawn up and someone metaphorically on the courthouse steps all set to file as soon as they got the phone call saying Goodell had upheld Goodell's suspension of Brady. (In actuality it was probably all done by email and web form submission, but the point remains). There's no way Brady's side could have beaten the NFL to court.
That said, since Brady's employer is in MA the MA court may have been less likely to give in to letting it go to NY since there's at least a linkage there. However, filing first still gets a lot of weight, especially when the filing was in an unquestionably appropriate venue.