Is adiabatic quantum computing as powerful as the circuit model?
Two quick clarifications:


Adiabatic QC is typically "based on qubits" just as much as circuit-based QC is -- I don't know where you got the idea that it isn't!  (Though one could also use qutrits or other building blocks, in either the circuit or the adiabatic models.)
As Mateus pointed out, the justly-famous result of Aharonov et al. says that "adiabatic QC is equivalent to standard QC."  But that result needs to be interpreted with a bit of care.  It holds if the final state of the adiabatic computation can be arbitrary -- so that, in particular, the final state can encode the entire history of a circuit-based quantum computation.  However, if the final state needs to be a classical computational basis state---as it typically is in the adiabatic optimization algorithm (the "original" example of adiabatic QC)---then adiabatic QC can certainly be simulated in the circuit model, but the reverse is not known and is far from clear.  So with the latter assumption, it's possible that adiabatic optimization really does give rise to a new complexity class intermediate between BPP and BQP.