Xiaomi offers amazing phones and does not brake the bank. I recommend you to add it on your list. 
This brand of phone is a beast when it comes in their processors and battery efficiency. I am a user of xiaomi smartphone and i can say that i just buy it in a cheap price but its like an high end smartphones in the market. The only thing that i am able to not satisfied with this brand even if it is a good brand of smartphone is their camera.