Your best climb rate is at your best lift to drag ratio but your steepest climb angle will always be near stall speed.
Lift to drag ratio does not change much for the wing - both scale like the air speed squared. The wings do not do much for climbing - they only provide enough lift to counter gravity. The steeper the climb angle, the less lift is required from the wings. What matters to climb is excess power and that just depends on total drag and effective engine power - assuming that your wings are capable of producing the minimal required lift, which places a limit on minimum speed to fly at all.
Speed for steepest climb angle also depends on excess power. The less excess, the closer it will be to the best climb speed, otherwise the plane will not climb at all.
edit:
about the P-38, it does not climb at a very steep angle - not in a steady climb that is. What it does is maintain control down to very low speeds due to zero torque and effective flaps. So, if it zooms with a P51, even if they zoom climb wing to wing, the 51 will flip over much sooner if it goes steeper than its steady climb angle. Yak for example will flip over at around 90 mph if it keeps full throttle, or throttle back in order not to flip, but then lose the engine pull to keep it going up. The yak compensates by having a crazy climb rate at 90-100 mph that keeps the climb angle very steep -
steady climb angle!
