Powering LED Strips with a Constant Voltage Supply and Constant Current Driver
I'm going to suggest that the constant-current driver isn't appropriate for your particular LED strip.  PWM is your better choice.

The reason that I'm suggesting that constant current isn't appropriate can be seen if you connect your LED strip to a variable-voltage power supply and slowly drop the voltage.  You will see the brightness start to drop and then you will see that some LEDs are brighter than others.

The lower the supply voltage, the more the brightness disparity will be.

The reason for this is that the LEDs are not identical.  Even if they came from the same manufacturing batch (they most likely did), there are still minor variations in their forward voltage.  This isn't a problem when there is significant voltage across the current-limit resistors.  However, reducing the supply voltage reduces the voltage across the series resistors and now the individual LED forward voltage variations become noticeable.

And that's what that variable current supply is going to do.  As you drop the total current into your LED strip, the voltage also drops.