I've not used the Ashdown comp, but what your asking of a cheap compressor is probably too much. If the volume difference between the two is significant without compression, you'll struggle to get a sound your happy with due to the sheer amount of work being done by the compressor.
For this task, the built in single knob approach will never work. you need either a very good compressor that has attack, release gain make up at least, or simply switch between 2 pre amp setting depending on which ( fingers or pick ) you're using..
If you wanted to compress both styles equally this would need to be done after the pre amp volume correction ( FX loop for example )