After playing some mission mode, I'm pretty happy with Purples and Whites being only in there, and not in the campaign. The other five types, they really lend themselves to unlocking parts of levels or serving unique traversal/battle/puzzling situations. Purples and Whites, though, their abilities improve your efficiency, but not much else.
The Purples have lost their impact damage and landing stun, which I'm okay with, since it was hugely overpowered, but also because the rock pikmin are a much more refined implementation of that kind of ability. So all they're left with is their 10x carrying strength. Not particularly useful in the campaign, but indispensable in mission mode. If you've got an area with a variety of buried things, you can just throw a single purple pikmin at it at the beginning of the mission, and walk away. They'll eventually dig it up, and whatever it is, they'll carry it back to the base all by themselves with no trouble.
White Pikmin's ability to dig things up is no longer special, since all Pikmin can do it now. They do a lot less poison damage when eaten vs Pikmin 2, and their poison immunity doesn't accomplish anything in a game with no poison. So their only remaining valuable skill is speed. Again, this is great for mission mode. Throw white pikmin on anything that's really far away from your base, that you want to get back sooner. I can't tell if they're useful for mining piles of gold though, because it looks like all of the Pikmin move at max speed when they carry those little things, but I haven't really done a proper comparison yet. If they indeed move faster there, that's a great use for them.