Current sensing on positive or negative end
There is no fundamental difference.

There are practical differences however. Generally, most people like everything connected to ground, I know I do. That then leaves a choice for which circuit elements are not so connected.

We almost always connect the PSU to ground. Often, the load is ground connected. In that case, you cannot use the second configuration, and have to use the first. Any load switches, controllers and current sensors all need to be on the positive side.

If we have the luxury of a floating load however, then we have the option of using a ground connected current sensor.

It all depends which components you can get, feel most comfortable using, or what your existing system configuration forces or allows you to do.