Most schools will use the higher FAFSA number. This happened to us (and it made a difference of $7 or 8K the first year - OUCH- based on the estimated IM EFC from College Board's calculator vs the FAFSA EFC). Apparently if the school is giving you any Federal aid (Stafford or Perkins loans, Work/Study), they are not permitted by Fed. law to use a lower EFC. A few schools, in particular some of those in the President's 568 Group, realize that this is unfair (since they feel strongly that the Consensus Methodology - a modification of the IM - that they use is the most accurate assessment of a family's financial strength) and they do a work-around by offering only institutional aid to such families caught in this situation (i.e, higher EFC from FM vs IM). They give institutional (not Federal) loans and campus jobs that are NOT Federal Work/Study to these students.
The only school where I could find specific details about this situation (of institutional only aid) is Amherst - they call such aid "Amherst only" aid: https://www.amherst.edu/media/view/1...Aid%2B2009.pdf
There may be a few other schools that do this (I'm not finding it now, but previously something on the 568 Group's website mentioned that some of their schools do this, without specifying which ones), but I couldn't find out which ones after spending a fair amount of time poking around the interwebs a few months back.
I did find a few schools (Tufts and Brown come to mind, IIRC, possibly also Reed) that specifically mention on their websites that, unfortunately, if the FM EFC is higher than the IM EFC that they must go with the higher EFC as required by Federal law.
Sure would be nice if more schools did as Amherst does... It's only fair that the same methodology should be used for all students.