One style is appropriate for interacting with the public and one is not. I think that is pretty obvious.
I actually just noticed this line - and I think perhaps there's something you're not realizing.
The guys you posted pictures of in full tactical get up - are not there to interact with the public. They're not there to help find your lost dog or give you directions. They're posted outside of high-value targets. The picture you posted of the cop standing outside the path station? Within a 1 mile radius of that you have the World Financial Center, Federal Courthouses, City Hall, The Holland Tunnel, Staten Island Ferry, the stock exchange, several high schools, several hotels frequented by various foreign entities (such as the Millennium Hilton directly across the street from where that cop is), the federal reserve, and that's just what I can think of off the top of my head. (I used to work down there, and have probably walked past that exact cop many times walking through that train station).
I know my last post on this was probably a bit sarcastic - but really, I mean - what exactly do you expect them to do? Any one of the places I named would make a pretty big target if someone wanted to come over here and cause some havoc. Should we taken the Indian approach and let someone take control of one of these buildings before calling in any kind of force?
They're not harassing average people. In fact, if you have to talk to them or deal with them for some reason (such as asking directions) they're actually quite friendly.
I also find it interesting that the picture of the woman in a "regular" police uniform is okay, while the guy in the "tactical" getup is not. It's interesting - because they're both holding AR-15s.
Aside from accessories - can you tell me why one is acceptable and one is not?