Robert,
I have both. It's a struggle for me to describe the difference I see and feel. The RX1 "feels" more solid and metallic than the A7R. The fixed 35mm f/2 lens on the RX1 has the weight and density of a normal Zeiss lens while the native 35mm f/2.8 lens for the A7R is plastic and less dense. The battery door of the A7R is flimsy and has a poor latch mechanism, compared to the RX1. Countering that, the A7R SD card slot can be accessed without removing the camera from the tripod. The irony is that in a shooting day, using 64GB cards, I'm more likely to have to change the battery than change the SD card. The overall fit and finish of both cameras is very good, and no bits have fallen off either camera (yet).
Of course, the RX1 has fewer buttons and dials, and its buttons and dials are easy to access. The A7R has some buttons that are made for tiny fingers, but that doesn't address your question about build quality.
BTW, I'll likely sell my RX1, now that I'm satisfied with the A7R.
Joe