Shunt resistance VS Rogowski Coil in current measurement , which one is better?
Rogowski coils measure only AC current. If you're measuring DC power, they are 100% not applicable to you. I've made use of several Rogowski transducers in my workplace, and have found that the coils can be quite fragile.

Shunt resistors can be used for AC or DC current measurement. For AC applications, it can be preferential to use a current transformer instead of a shunt, as it introduces less losses in the circuit under measurement (assuming your single-turn primary is of sufficient size).

Hall effect sensors are good for AC or DC as well, but the ones that I've used need + and - DC biasing, and can be cost-prohibitive at lower power levels.

Given your range of current, I suggest that a hall effect sensor will be your best bet in terms of accuracy, size and losses.