They are both nominally the same maximum output power but are very different chip sets.
Personally I have had two AR300M’s communicating easily in clear direct line of sight at a range of 200 metres.
Indoors this is very different and depends on so many things. Old buildings tend to be better than newer in my experience.
I have replaced a couple of old MT300N (version 1) with AR300Ms. The coverage in a fairly modern building, between numerous walls was dramatically improved over the MT300Ns, presumably the receive sensitivity is better? This might of course be reversed in different building construction/layout situations as this was by no means a scientific test. Just my experience in specific cases.