Here since the 1980's they connected most of the signals to a central control room with an upgrade to a computerised control for each intersection. This replaced the old Automotor controls, of which a few are still left running small intersections. That way they can remotely program light duration and have traffic pattern control.
all of ours are independent, due to the distances that they are apart.
there is no "control room", but the spec is (state law in my state, ymmv) that if the signals are less than x amount apart, they must be connected to a common controller to synchronize them for better traffic flow. still all computer controlled and autonomous though.
actual power consumption differences between both methods, i cant say, i dont pay the electric bills, and im not privy to that financial information, but under the guise of reduced power consumption, we were mandated to retrofit all of our incandescent bulb signals to led's a few years back.