From what i hear from our maintenance the airbus ISIS and the boeing ISFD is basicly the same unit build by thales. However since the connectors are set up differently they are sadly not interchangeable between fleets which makes it necessary to stock both parts in my operation. Dunno about the airbus setup as i haven't been able to crosstrain yet but on the boeing 737 as mentioned above the heading is supplied by the left IRS only, however there is a note saying that you have to validate that heading information by crosschecking with the magnetic standby compass. Additionally it receives ILS information from NAV 1, altitute, airspeed and atttitude are computed internally.
Interesting enough the ISFD is powered by the battery bus (no surprise there) and cannot be put offline as it has no circuit breaker.