Why are watts used as a measurement for some appliances?
There are two principal AC mains household voltages in use in the world today, (120 and 240 volts) and the appliance's voltage rating is given in order to indicate what input voltage the appliance is rated to support.

Watts is specified since that's the work that's being done by the appliance when it's ON, and that's what your power company is charging you for. 

EDIT/UPDATE:

In the examples you've shown, the juicer ad is non-deceptive in that it discloses how much power it uses and, knowing that and what your power company charges for energy, you can determine its run cost.

For example, if your power company charges 10 cents per kilowatt hour of energy delivered to your home and your juicer uses 1 kilowatt, (1000 watts) then for every hour it's ON it'll use one kilowatt-hour of energy and you'll be charged 10 cents for that.  Not a bad deal, and to look at it another way, if it takes you six minutes to juice some fruit and your juicer is running balls-to-the-wall, that'll cost you a penny.

On the other hand, there's nothing to be gleaned from the Sears ad since all that's mentioned is that the battery is an 18 volt NiCd pack, and that it has a capacity of 1.1 ampere-hours, which means nothing if the running current, under load, isn't specified.

It isn't, and even though the magical power number could be backed into knowing torque and RPM, the torque is specified, at 1700 RPM, as zero inch-pounds, shutting all the detective work down.

There may be more exhaustive data at DeWalt's site re. the performance of their drill.