TE flaps increase the camber of the wing which increases the CL MAX, but the greater curvature means the airflow separates at a lower AoA because it simply cannot make the sharper turn (as BEagle pointed out, the CL curve moves up and slightly to the left). This is true for TE devices that only increase camber (Spilt and Plain Flaps). More efficient flaps that also increase boundary layer energy (Slotted and Fowler Flaps) raise the CL curve even further and help to maintain the airflow to the wing at even higher CLs. Fowlers being the most efficient flap types also increase wing area.
The effects of LE devices depends on the type of device. A device that increases boundary layer energy (Slots and Slats) extends the CL curve, allowing a greater CL Max and an increased critical AoA. If the LE device increases camber only (Kreuger Flaps), then it does not extend the CL curve, but does move it up and to the left (having the same effect that TE flaps have). Slats increase the BLE and also the camber therefore extending the CL curve and raising it as well.
Next time I pull out my aerodynamics book, remind me to wear a dust mask
