Change in duty cycle of a transistor (BJT)
Compare your circuit with a non-saturating version: 







simulate this circuit &ndash; Schematic created using CircuitLab


You may have to add some resistance in series with the LED to keep the transistor power dissipation low enough to use a small transistor. 

The cause of the slower turn-off than turn-on is saturation of the BJT. As you can see the duty cycle (in terms of current) is higher than the input duty cycle. Since LED current is what generates the light, that means you're getting more light than would be expected from the PWM duty cycle. 

Another way of preventing saturation is to use a small (low capacitance) Schottky diode from collector to base. That is a version of the classic Baker Clamp.