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I've been using Layer Paint since my Note 1, it's a bit more like Paint Tool SAI rather than PC Photoshop.
It has layers and has a nice pen mode that'll disable touches for painting. (Touch is then only used for pan/zoom).
There is a free version (Layer Paint Zero) but I've never tried it so I can't tell you if there is a difference or not.
LayerPaint and LayerPaint HD (for 7" and up screens) are absolutely fantastic.
Clover Paint is also fantastic because of how damn customizable it is (seriously you can make your own brushes and quick select buttons for them, even export and share those brushes with others), but that is also it's downside. It's damn complicated.