Pikmin 3 will play in a similar fashion to previous installments. However, the Pikmin themselves will be able to preform a multitude of different tasks. There are new hazards such as ice and magma-based enemies. Olimar, for a reason Miyamoto wants to stay secret, was not a playable character during the E3 demonstrations. Instead, a pink-haired girl, a bald general, a small blue haired boy and a tall, green-haired man are the playable characters. 
Pikmin will break walls differently based one where they attack walls, and the various other new tasks can be performed, such as picking up fruit and anything else used for nourishment.
The captains will be able to throw other captains and appear to be able to play with eachother in the main story mode.
The battle mechanics will be much more refined. Some enemies will take more damage if pikmin are thrown onto specific parts of their bodies. Two control options are currently available: The Wii U Gamepad and the Wii remote (with Wii MotionPlus) & nunchuck. The players will be able to use the Wii U Gamepad to view different parts of the map. The Wii remote & nunchuck configuration will control similarily to the Wii versions of Pikmin and Pikmin 2. One key difference is the omission of the ability to move pikmin around the pilot as a group.
There will be many new game modes, including multiplayer, singleplayer, and a new type of Challenge Mode.
In the E3 demo, many critics took note of the fact that the "swarm" feature appeared to be absent from the Wii Remote and nunchuck control scheme. It appears have been altered somewhat; the player can use a flicking motion with the nunchuck to make the pikmin charge at a target. This is mentioned by Miyamoto during Nintendo's E3 2012 press conference, and it is seen briefly in the first game trailer. A new ability has also been added; captains can now quickly roll side-to-side, and any Pikmin following them will do the same.
The game was confirmed to have an additional Multi-player gaming mode. It will not, however, have the online multi-player capabilities other Wii U games have displayed, due to complications such as too many screens dropping and having so many Pikmin, may cause lag in the pikmin's unique movements. 
So far, 2 new Pikmin types are available:
According to a woman at the E3 showfloor, there will be additional Pikmin that will be discussed about at a later date. 
Miyamoto was questioned in a recent interveiw about the absence of the Pikmin from Pikmin 2, particularilly, the White Pikmin.
He jokingly stated "They're in there...they're just hidden."