I have the "lobster" one.
I actually prefer the cave missions, mostly because they add challenge. The overworld is where you explore and raise Pikmin... the caves are where you use them, sort of like dungeons in an RPG or pretty much any game with dungeons.
There is no challenge to the enemies on the overworld, because even if you lose all your Pikmin you can just raise new ones. The first game got past this with the time limit... Pikmin 2 gets past this with the caves, where you can't raise additional Pikmin and every Pikmin counts.
I love the feeling of picking my 100 best Pikmin to venture into the unknown. It fulfills my "commander of crack covert ops squad" childhood fantasies adequately.
I bought Pikmin 1 but never got far into it because the time limit put me off... I hate time limits. I can already tell I'm going to be hooked to this one till I finish it though.