1. I have a circuit which has power coming from Vusb or Vbat. Current is 700mA max.
2. When power from Usb is coming, device should run on Vbus and Vbat should not come in picture, as soon as Vusb removed, then device should immediately run on Vbat without fluctuation.
3. Made this circuit, going to test it, any comments on it?
4. Here is updated design, battery voltage range is 2.4V to 4.2V
5. Vusb is +5V

 

What are the voltage requirements of the load? The supply voltage varies from almost 5 volts to a bit below 2.4 volts, and that is a quite wide range. And is the load current max 0.700 A for much of the time, or just occasionally?
I have not studied the specifications of that FET, but the circuit looks reasonable.