Well, that's nice.
However, considering who is running NYC (and the historical MO of the bureaucracy), I think the "changes" will be merely cosmetic, not actually something to allow more citizens to get permits.
NYC is a great place for some foods and entertainment, but if you like to own and use handguns, while it may not be the absolute worst place, its way up there on the list. I had a NY State permit back in the 1970s, not valid in NYC, and it took 5 sets of fingerprints, 4 photographs, 3 character references, and a couple months of wait. And that was for mere posession and open carry only! And only the guns listed (by make, caliber, bbl length, and ser#) on the permit could be posessed!
And on top of that, nearly 30 years after I had left NY, they tracked me down, and sent me a letter stating that, since I was no longer a NYS resident, they wanted the permit BACK! YES, the little card! And, they wanted to know what happened to the guns listed on it! I thought that just a tad obsessive. And that was from an "upstate" county!
I doubt that the move by NYC is anything more than smoke and mirrors, intended to make us think they are doing something good.
All else being equal (and it almost never is) bigger bullets tend to work better.