Some aspects are:-
Redmi Note 3 costs ₹11,999. It has 5.5 inch full HD display, snapdragon 650 processor, Adreno 510 GPU, and rest of features are similar to Redmi 3S Prime.
Redmi 3S Prime and Redmi Note 3 also have second model. Redmi 3s Prime costs ₹6,999 and note 3 costs ₹9,999. Both offer 2GB RAM and 16GB internal memory. While ₹6,999 Redmi 3S Prime do not have fingerprint sensor.
Some features of Redmi 3S Prime better than Redmi Note 3:
Camera- Even if megapixel counts of Redmi 3S Prime are lesser than Redmi Note 3 but it still perform lot better. Capture Speed of Redmi 3S Prime is noticeably faster and photo quality is also better.
Weight- On paper Redmi 3S Prime has managed to be litter than Redmi Note 3. Redmi 3S Prime has weight of 144 grams while Redmi Note 3 has weight of 164 grams. But practically Redmi Note 3 feels litter because of its large size weight gets distributed over hand more than Redmi 3S Prime.
Thickness- Redmi 3S Prime is thinner than Redmi Note 3. It has thickness of 8.5 mm while note has thickness of 8.7 mm. Difference in thickness is noticeable but it’s little. It wouldn’t matter much if you don’t care of thickness.
OS- Redmi 3S Prime has recent Android OS 6.0 Marshmallow and you can hope for latest Android OS 7.0 Nougat in future. Xiaomi say it has MIUI 8 but it comes with MIUI 7.5 and it could be upgraded to MIUI 8. While Redmi Note 3 has Android OS 5.0 lollipop and MIUI 7.5 and it will get MIUI update in future which will have Marshmallow.
Portability- Redmi 3S Prime is more portable than note 3 due to its display size, weight, and thickness. 5 inch of screen is perfect, 144 grams of weight, and 8.5 mm thickness is charry on top. If you care of mobility more than performance so this is the best option.
Performance- Redmi 3S Prime and Redmi Note 3 perform relatively same. There is not huge difference in performance.
- Even if Redmi 3S Prime really well but it doesn’t provide one basic feature and that is backlit key at bottom. It do not provide baclit menu, home, and back keys instead it has capacity key which won’t glow. This could be real pain for some people which suffer finding capacitive keys in dark at night. If it's completely fine for you then it's the great option.
- Xiaomi has not specified anything about its screen type (soda glass or gorilla glass or dragontale glass). But it has some protection to key scratches.
- There are some bugs in MIUI but it will probably solved by upgrading to MIUI 8.
So which smartphone to buy?
Definitely you should buy Redmi 3S Prime its great value for money. You could save some money and buy good accessories for your mobile.