Hi,
what is the measurement used for?
Just coarse current measurement, regulation loop, short circuit detection, detection of DC voltage, phase shift detection, ....
Is the measurement timing critical (delay, phase shift...)? (limits..)
What is your decided ADC sampling frequency?
I wonder what´s the idea of using a current sense amplifier with 300kHz followed by a 230,000kHz amplifier.
I mean it´s almost 1000 times the frequency.
On first sight, I´d go with the first circuit.
But it really depends on what signal information you are after.
Klaus