They are more expensive, they are more complicated and a well build AC pump is inherently more efficient.
I would have stopped at the first two (expensive/complex). "inherently more efficient"? Yeah, about that. Small, single phase induction motors are about the least efficient electric motors there are. Especially compared to BLDC motors. The little AC power heads are worse, but...
Look at the specs for a 1/15 HP (i.e.: 50w motor) Dolphin Amp Master pump. Only 50w of work output, but pulling an average of 1.21amps at 120V, or 145w electrical input. That works out to about 35% efficient. There are worse, but that isn't great.
A generic BLDC (aka: "DC Motor") pump is going to range between 60% and 80% electrical efficiency at the motor depending on operating point (three phase motors are always a LOT more efficient than single phase motors). The 24VDC (or whatever DC power supply) is going to be between 90 and 95% efficient these days. So worst case, you are looking at .9 * .6 = .54 or 54% efficient. And could be as good as .95 * .8 = .76 or 76% efficient. There will be a small loss in the controller as well, but that is really low these days (notice how small the controllers are and the fact that generally don't get hot? Efficiency).
The BLDCs motors are just a lot more efficient than a good fractional hp single phase induction motor and a LOT more efficient than the (shaded pole?) AC power head type motors.
But the DEFINITELY are more expensive and more complex (more things to go wrong). But they are not "inherently" more efficient.