A power attack command (named after the dnd feat of the same name) allows you to prep a special attack during combat; this requires a skillcheck against fi.sp.we. After some amount of time has passed, the special attack will attempt to fire. It is like a basic attack, but more damaging and less accurate. Like a basic attack, it uses the relevant weapon skill. Note that during the waiting period, you do not have to stay next to the target; you may prep the command, leave the room, and then return, and the special will fire if you were fast enough.
Most of these commands cost 35 fighting points. Some cost 45 and are restricted to the warriors' guild; these attacks do more damage. Since the damage one of these commands will do is dependent on arbitrary weapon data (that is, a single weapon may have two commands and do different damage with each) which can't be measured, it is effectively impossible to directly test how much more damage; the belief that the warrior only commands do more damage is based on the word of the creator base and indirect testing (that is, most weapons seem to do more damage with their warrior commands than their nonwarrior commands). Current prevailing wisdom holds that they do roughly 10% more damage. Since they cost more than 10% more gp to fire, this would make them less efficient - a warrior specialing as often as possible would do more dps with a nonwarrior command.
Power attack commands divide by damage type; that is, a given command always deals the same type of damage.
As a rough rule of thumb, chop and hack tend to be used with weapons requiring less finesse, such as an axe, while slice and slash are used with weapons such as a sabre. There is no meaningful difference between them; likewise, bash and smash are the same, as are pierce and stab. Ignoring damage type, all of these commands will behave the same way; likewise, crush, impale. and behead will all behave the same way, except for behead's special behaviour, as noted above. Again, these are all based on arbitrary weapon data; you may find weapons which have e.g. both chop and hack and do different damage with each.