The implemenentation is DRASTICALLY worse. The note 4 has similar shutter response to the iphone 5s. The 6 is much much better at moving objects.
If OP wants to sacrifice photo quality that is one thing. He says he does not. I don't know how you can reccomend an android phone to somebody that walks in saying "shutter speed, auto focus, performance" and say Note 4. Note 4 takes more detailed still pics in good light, that's about all it does better than the 6 plus.
Take all the reviews, and average them. The iphone is a vastly superior phone for taking pics and everyone here knows it.