Really good question! For passive systems, they are nearly equivalent functionally. N-Channel applications in low side are often cheaper because manufacturers make billions of N-Channel per year (scale economy). So if you make thousands of your products saving a couple cents per device can add up. Sometimes you might not want a large volume device in the lowside/return loop area for layout reasons. That is to say, your board real estate might not resolve to something that fits the device geometry near the ground loop termination. I've done boards which it made more sense to place a reverse polarity application on the highside area compared to lowside area because it optimized the space usage better for the board. N-Channel applications require all voltages to be referenced to a separate ground node which you might not like to manage...so there's a "true ground" and "protected ground." N-Channel devices almost always have low ON-state resistances compared to P-Channel devices so N-Channels help prevent system power losses which is good. I think one disadvantage of N-Channel devices that comes to my mind would be if you have a lot of other switching circuit subsystems going on that are referenced to the protected ground. The series inductance and stray/parasitic capacitances of the N-Channel device in that ground loop position might react in a way you wouldn't expect. All the current aggregates at that N-Channel device as it exits your product. So, if the current has frequency content, it could do something weird. You'd have to look at how your switching systems interact and how their loads behave which would manifest the potential frequency content. Adding either reverse polarity device changes impedance of the lines so it's a good idea to think about how you might balance it in either application.

You can use this to protect an inverter circuit

well, with the way you've communicated, it's a very generic question. If you can narrow it down for me I'd appreciate it. Usually, problems with limits tend to be about naming things. It's likely that you don't have an "OUT1" or "OUT2" node in you circuit...so MC12 would choke in that case because its trying to process something that isn't there.