I own a few pairs of the Pioneer BS-21s and several of the little Dayton and Lepai class D amps. I also own a pair of Audioengine A2s with the little wedge stands that I use on my desktop. I seriously considered another Pioneer/Lepai setup for the desk, but I decided against them for the reasons below.
So... Would the Pioneers + a D-amp sound better in most applications than the A2s? Yeah probably. But on a desktop? For that I'm less sure. They're really big. And the waveguide around the tweeter pushes the CTC distance pretty wide. Extreme nearfield listening is going to put you pretty far off axis for one driver or the other. How far are the speakers going to be from your ears? As for the bass, I've found the A2s completely adequate. I think the reinforcement from my desk and monitor help.
Then there are the practical considerations. The Pioneers are seriously big for a typical desktop setup. Do you have room to put them on your desk? Far enough from your head to avoid being far off axis for one driver? Without putting their rear ports all the way against the wall? I don't, but maybe you do. The A2s are signal sensing and go into a low power usage mode when they aren't being used. Will you leave the Lepai amplifier on all the time (with its overly bright blue light ring), or will you turn it off when you aren't using it? For me, I was pretty sure I'd end up leaving it off much of the time and have no sound at all. Then when I did turn it on, I'd forget to turn it back off when I walked away from the computer.
And last is looks. I like the look of the Pioneers, but them plus an amplifier on my already crowded desk would have just looked silly. And the A2s are the cutest little speaker I've ever seen. In person they just look fantastic. Their finish and level of visual refinement is a definite step above the Pioneers.
Anyway, that's how I made my decision for desktop sound. I hope it helps. Good luck making yours.