One of the main difference is Processor. RN4 uses very efficient Snapdragon 625, while Redmi 4 uses Snapdragon 435. Not much reviews are out for S435, S625 has got very good reviews in budget segment. Moto G5 Plus, Lenovo P2, Moto Z Play all comes with S625. Battery efficiency is very high for S625.
Another notable difference is Display. RN4 comes with Full HD Display, while Redmi 4 has only HD display. Also the screen size is different. RN4 is 5.5" & Redmi 4 is 5".
These are the main difference. All other specs are almost same.