The automatic feedback destroyers are parametric EQ devices and can have notches that go as narrow as 1/60th of an octave so that minimal colouration of the sound is made. However these devices rarely pick a band that narrow and if left in auto mode have a tendency to widen the band as time goes by - which can totally mess the sound up.
So I thing everyone else will also recommend you to go for 31-band graphics. There are 31 band EQs with the power switch on the front (if that is vital to you) so have a bit more of a look around. You may get away with a 15-band graphic for gentle FOH sound balance adjustment but it will still be too crude to deal with troublesome room modes.