In terms of specifications, they are almost same, except for a few other specifications. One of the most talked about change in specification is the processor. Redmi Note 3 had Snapdragon 650 where as Redmi Note 4 has Snapdragon 625. While opinions are varied in the online forums, it is asserted that the processor on Redmi Note 4 is a balanced and less battery consuming than the former Snapdragon 650. Another specification that is being talked about is the reduced mega-pixels on Redmi Note 4 which is 13 MP compared to 16 MP on the Redmi Note 3. Although the resolution has decreased, Xiaomi has used a better sensor with 1.2-micron pixels compared to 1-micron sensor on the Redmi Note 3. This Redmi Note 4 has larger pixel area to capture more light and improve the image quality. As image quality is not only about the Mega-Pixels, this reduction in MP should be be an issue.
Here is a short video on comparison of Xiaomi Redmi Note 3 vs Redmi Note 4
Most reviewers believe that though it may look like Redmi Note 4 is much of an upgrade from Redmi Note 3, Redmi Note 4 is a refined version of it's predecessor with improvements in battery life, better performance and improvements in camera quality. The performance of Redmi Note 4 has been awesome in the last 5 days we'd used. Multitasking is smooth without any lag. Battery life is much better than most phones in this price range. Gaming is good too on the Redmi Note 4. Even heavy games could be placed on it with ease, but if it is the 2GB RAM variant, it is ideal to play heavy graphics games in medium quality.
However, if you already have a Redmi Note 3, then Redmi Note 4 may not be an ideal upgrade as the features are comparatively not that much of a difference.
Xiaomi Redmi Note 4 scored an impressive 62468 on the Antutu Benchmark tool with the 2GM RAM variant.
Overall, the Redmi Note 4 phone can be termed as one of the best mid-range Android phone to buy. It is loaded with features and should not disappoint any with the package it is loaded with and affordable price tag.