As far as I can see looking at the actual ISO document.  The only difference between ISO 15919 and IAST for transliterating devanagari sanskrit  is the letter for anusvara. M with dot on top versus m with dot underneath.

Is part of the reason for Sanskrit scholars opting for IAST instead of ISO 15919 that the ISO 15919 document costs over $200.00 and is not publicly available.

Thanks,

Harry Spier