Best Rate is based on excess power and best angle is based on excess thrust over what's available for straight and level flight.
Vy occurs at a higher airspeed than Vx and Vx occurs at a higher AoA than Vy so more induced drag at Vx.
Just think of rate being work done over time, so even tho the angle of climb as we look at it from the ground looks steeper, and it is, the best rate of climb gives us the best climb performance both vertically and horizontally(over a period of say 2 mins) mainly due to there being less drag to overcome at that angle of attack.
Several books cover it pretty well Bob tait for basics and mechanics of flight for something a little more in depth..
Last edited by Homesick-Angel; 27th June 2013 at 23:26.