The Cosair VS650W is a 240 Volt Power Supply where as the Cosair RM650W is a 120 Volt Power Supply. The 120V is your standard three prong outlet that you would plug maybe a vacuum cleaner in or a power strip into. The 240 is like the power cord off of a washer or dryer. So you would have to have a special plug for the 240V Power supply.
There really isn't a difference in efficiency. With the 240V you are capable of pulling a lot more power than just your standard 120V. However...since you are only wanting 650 Watts...there isn't a reason why you should use a 240V power supply. If you were wanting a 1300W + power supply...you would need a 240V Power Supply to be able to pull that amount of energy from the socket.
Bottom Line, the...