Sealed box designs need more amplifier power, on the whole, because the cones have to work against the very stiff spring of the air trapped inside the box.
Although stiffness is provided by the air in the sealed box, the spider on a driver designed for acoustic suspension is less stiff, and compensates.
When Vilchur designed the acoustic suspension speaker he modified the driver spider to provide less spring restoring force on cone excursion because he knew the air in his sealed box would provide some restoring force.
The main reason the acoustic suspension speaker needs more amplifier power is the energy of the back wave is totally absorbed by the stuffing (converted to heat). In a reflex design, the out-of-phase back wave energy hits the port and is inverted 180 degrees, and is now in phase with the sound coming off the front of the driver. This extends the bass response, although the eventual rolloff when it does occur is much steeper (typically 12dB per octave as opposed to 6 dB per octave).
There are many good speakers using the bass reflex system.