One of my favorites out there today is the A10-OLinuXino-LIME.
The Beagle Bone was good in its day, but it is kind of over the hill. The processor is underpowered compared to other ARMs
Just to be clear, the A10-OLinuXino-LIME, BeagleBone white and BeagleBone Black all contain a single Cortex-A8 core, and the TI AM3359 runs at the same 1GHz speed in the BBB as the Allwinner A10 does in the LIME.
The original BeagleBone (white) ran its AM3359 at 720MHz so its CPU performance is a bit less, but the BeagleBone Black (BBB) superceded it a year ago and at a much lower price. As a result, the reasonable current-day comparison is between A10-OLinuXino-LIME and BBB, and on CPU power their similar speed Cortex-A8 cores make them pretty much identical.
I have all of these boards and many other similar ones, and my assessment is that BBB is much more capable for embedded projects because of its additional dual realtime 200MHz PRU cores (which are quite unrivalled), while the A10-OLinuXino-LIME is more suitable as an extremely low end desktop-style "computer" because of its dual USB2 host sockets and rather more capable MALI-400 GPU.
This assessment doesn't change when the just-released A20-OLinuXino-LIME is brought into the comparison, except that the dual Cortex-A7 cores in the A20 make it a far better general purpose "computer" than its A10 sibling for a mere 3 euro more in price.