it sounds to me like one is a MTB or ATB and the other a road bike.
is your Bianchi black or new rose (light red) colored? it is not a Campione del Mundo it is a most likely (unless someone swapped the components) an '87 Sport SX. which was not only my first Bianchi but first new "10 Spd" if you like riding on the road keep the Bianchi it is one great bike.
if you need a errand / beater bike keep the Giant
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“One morning you wake up, the girl is gone, the bikes are gone, all that's left behind is a pair of old tires and a tube of tubular glue, all squeezed out"
Sugar "Kane" Kowalczyk