It was a rivalry in 1971. Since then, the league added the Islanders, Devils, Capitals along with the Flyers who entered in 67, and for about 18 years the Whalers. So the Bruins and Rangers were geographically the closest rivals in the league since the 40s and now the Rangers have like 4 other teams within a short train ride from them that take up much more of their limelight. All the while the Bruins have been much more hung up with Montreal and in the last decade with Toronto and Tampa. The playoff format has only resulted in them meeting once in 2013, which was a snoozefest gentleman's sweep of a series most notable for Torey Krug debuting due to all the injuries on the blueline and scoring like 4 goals. There wasn't a lot of juice or hard fought emotion in that series.
If the Bruins get past Montreal in 2014 and they met in the ECF as they should have, maybe a rivalry develops. But maybe not.
NBCSports always tried to shoehorn Bruins/Rangers games into their "Wednesday Night Rivalry" series but that's a shallow ratings ploy. The teams just never interact enough for it to matter. It'll take multiple playoff series or a particularly heated one for it to develop. Even then, Rangers have two natural rivals in their backyard who will always get more attention from their end and the Bruins are concerned with other teams as well.