What’s the difference between led current draw with and without PWM?
A led had usually two kind of max current specified in its datasheet: Pulsed and DC operation. Usually, max pulsed current can be much (e.g. 5-10 times) higher than max. DC current. 

If you consider only the current, you will have the same result if you operate 1A at 100% or 2A at 50% (Both have 1A mean current). 

But because the forward voltage of the LED is higher at 2A, you will generate more heat losses at 2A/50%. 

It could be that you have more brightness at 2A/50%, because the current to brightness curve of a led is not linear.