I'd say a shunt is more accurate. But with it's low signal voltage you need to take care with amplifying the signal.
A wrong designed amplifier or a bad layout could easily make the overall performance worse than the CT.
5 (100)... For sure you could find reliable information in the internet.
I guess the 5A is for continous RMS current, the 100 is the peak current. But i'm not sure..
100(5)A means 100A primary (input/measured) current and 5A (full scale) output current.
If you only need to measure AC currents (and you need galvanic isolation, too) a CT it's a better option, as it only requires a single external burden resistor (and maybe a simple rectifying/filtering circuit) to feed the output signal to your measuring circuit.