The first, We the people, strikes me as unitive. It creates in me a feeling of connectedness to others. We the people have a purpose, are willing to work together, are in some sense one. The other phrase, you people, moves in an opposing direction in my mind. It separates out a them that somehow is threatening to us. You people is binary, we the people is singular.
A few times in my life, I have heard you Catholics followed by a statement that I found surprising, sometime offensive. Those experiences function now as warning bells against the very human tendency toward tribalism. I see clumping another group into you people, whether I use those exact words or not, as heading down a wrong path.
It is not that I refuse to see differences: nationality, race, religion, socio-economic class, political leanings are distinct and do influence who I am, on a certain level. But three things warn me against taking distinctions between myself and others too seriously. The first is my experience of having been stereotyped and wanting to avoid inflicting such pain on another. The second is an historical awareness of the destruction that often grows out of out of an “us against them” mentality. The third is my baptism. I follow the One who taught we the people to say Our Father.