Yeah it really depends where and when you go over…
I have crossed near Watertown a couple of times in the past month or so, first time it was ID only and I was pretty much told I needed at least a copy of my BC…they pulled me over and searched my car (thankfully I’m not evolve) and then let me go…next time I brought both forms of ID and had no issue…
Though I have never had any problems with ID only at the various WNY crossings it is not a bad idea to have a copy of your BC with you to make things easier