LDO quality with current measurement shunt
With the shunt before the LDO, you'll be measuring not just the load current, but also the current the regulator itself takes to operate. This is likely to be a very tiny amount, but it can be significant depending on your application.

A counterpoint, though, is that having the shunt after the regulator reduces your load regulation. Higher currents out of the regulator mean a lower voltage after the sense resistor, because that's what resistors do. If the shunt is before the regulator, its effect will be mostly regulated out by the regulator doing its job.

So it's a tradeoff. Do you care more about accurate current measurement, or good voltage regulation? The answer to that determines where you should put your sensor. If you care significantly about both, then you need to start looking into other methods of current sensing.