I think this topic should really be in the headphone section to get more feedback from headphone users... however, I have this CDP and find it quite enjoyable. I've heard the Planet 2000 but not in direct comparison. I do not use headphones at all.
You may want to
contact Bill and see if he can provide a demo or trial to do your own comparison.
I haven't seen a lot of direct comparisons either. The only one I've done is against a Bel Canto DAC2, Museatex DAC, and Audio PC. Of the 3 or 4 people that listened, I think 3 or 4 opinions as to which sounded best were formed. I liked the Minimax but thought it was a little laid back. I liked the Audio PC best. I've since gotten new tubes and allowed for lots more break-in and am really enjoying it. The presentation is musical and involving.
I'm using Rocket Logo Russian NOS tubes from Upscale Audio that I think have the smoothest presentation of anything I've heard. I had Amprerex A-frames and round getters (both orange globe) that I tried but the Amperex seemed to be a little too harsh in the upper midrange which accentuated digital hash a bit. I was thinking of having the EE CDP's signal path completely upgraded by a modd'er at some point. I would do the Audio PC but I have decided I can't deal with another PC in my life.... especially not in the one place that's a haven away from such things.
In any case, I think the EE CDP would likely sound more natural to my ears than the Rega. Whether it can drive your cans, I have no clue.
-C