The saying goes Manhattan keeps on making it and Brooklyn keeps on taking it. It is well known that BK is NY's grimiest borough. Of course not everyone from the old BK is a savage. If Brooklyn were an independent city, it would be the second largest city in America.
But you also have to consider the time period when Jay first really started going hard with the music in 94-95'. Shooters in the 80's might have worn fitted clothes, Gucci and suits, but the NY street image portrayed by rappers in the mid 90's was nothing like that. Everyone in NY was making grimey unpolished raw street music and had the same army fatigue, Timbs, project life image and story from Nas to Mobb Deep to Boot Camp to Wu Tang. Jay stood out from all of them dudes.
Hov helped usher in the Jiggie era of the late 90's and was "the king of champagne bottles" as Nas said. DMX helped usher back the raw NY street aesthetic after Jiggie era Rap became too ubiquitous
but Jay stayed in his lane and never switched. But all that pretty boy shyt really started with Big's image being coached by Puffy and others in NYC mostly dudes not from BK. I read an article that said Big traded in his army jackets for Coogi sweaters and Kangols after peeping game from some big money dude from uptown named Walt G.
Notorious B.I.G’s Cosby COOGI jumper is now on sale | British GQ
To this day, people from other boroughs clown BK for being late on trends and shyt.

And to this day, the roughest parts of NY are still in BK. So you do the math on that one.