At least the GBA version will allow you to more readily farm alerts(the items that cause the rarest battle in an area to occur)...

Ie you farm 99 of them, go to the pink puff room, use them, only get in battles with pink puffs.. then go back to the place where you can farm them.. and get 99 more...

If I recall, there is no "place to go back to" once you are at the pink puff room on the PS1 version. Not sure about the original version.