No, from Palkia G Lv.X's Power, neither player takes Prize Cards for the Pokemon sent to the Lost Zone. However, in something like Giratina Lv.X's Attack, you would take a prize.
Effects can get you prizes, Crobat G, or Spiritomb for example. And gengar is an effect, and he takes prizes. (but in this case, no prizes are drawn, because it is not a KO)
^Those effects affect the Pokes' HP and/or status and are therefore different. Palkia states that they're removed from the board, not that a KO takes place or that damage is placed. Totally different.
Whenever an effect states something about discarding/removing Pokemon from the field, look closely at the text. Look for example at Regigigas LV.X from Stormfront. His power specifies that it gives up a price card every time you use it. Whereas Palkia doesn't. Look for that line at all times.