The slow response time in phones and tablets due to TFT LCD (Thin Film Transistor) made the evolution of IPS (In Plane Switching). The IPS overcomed the viewing angle problem in the traditional TFT LCD and was faster than TFT in response time. Additionally,color replication and sharpness on IPS LCDs were better than on the TFT. One the other hand, the need of strong backlights made IPS power hungry. IPS also resulted in making the screen bulky or thicker.
AMOLED (Active Matrix Organic Light Emitting Diode), an upgrade to OLED (organic light emitting diode) produce (emit) light when exposed to an electric current. In most cases, this helps to avoid the need for backlighting, resulting less power consumption and bulk screen. It provide better viewing angles, surpassing IPS. If you want deep blacks, nothing beats an AMOLED panel! However, the difficulty to produce AMOLED, makes it cost higher than IPS and images aren't quite as sharp. Another issue with AMOLED screens are that they aren't as visible in daylight as IPS displays. In addition, AMOLED dots degrade, reducing the color saturation of the panel over time.
The selection of better among them are not a set defined by any person. No one can say that one is clearly better than the other. The like and dislike of each user vary making the selection reasonable.
Hope you get an idea, Mr. Muhammad Haris. What you select is the best for you. Have a great time.