Actually, Mach4 is compatible with most Fanuc post processors that support Tool Compensation Memory Type C Fanucs. A Fanuc 21i is an example. We did this by design to eliminate anyone ever having to have a post processor expressly written for Mach4.
Mach3 had some differences from Fanuc that required its own post processor. However, For a mill, Mach3 and Mach4 are pretty compatible, G code wise. Mach4 is more strict about how the G code is written than Mach3, so your mileage may vary when trying to use a poorly written Mach3 post processor that doesn't implement canned cycles very well. I have no idea if the Fusion 360 Mach3 post processor falls into this category.
The main differences are between Mach4 and Mach3 are in the Lathe interpreter. Mach3 lathe G code will most likely not work at all in Mach4.
So if you want to avoid running into any of those type of issues, use a Fanuc post processor.
Steve