GRE at home vs. test center — which is better?

Neither is objectively better. The test center gives you a controlled, distraction-free environment with scratch paper and pencil. At home, you get the comfort of a familiar space, but you use a whiteboard or a sheet of paper in a transparent sheet protector instead of scratch paper, and you may deal with tech issues. Most students do equally well on either, so pick whichever setting makes you more comfortable.