Which dictates a control voltage between the sum of the transistor EB junction and the LED forward voltage drops, and 5V.
Not a very well behaved circuit. It will be interesting to see how you intend to bias the digital potentiometer to cover that range.
Same thing for the common emitter version, but with different problems.
If you think you will get a 0-max output from the LED from a 0-max setting of the digipot, you are in for some big surprises.