I would define fIf and fWhich this way, with explicit w variable:
fIf[u_, v_, w_] := Module[{aa = u + v + w, bb = 2 u - v - w},
r = Which[bb > aa, BB, aa > bb, AA, aa == bb, AB];
{aa, bb, r}]
fWhich[u_, v_, w_] := Module[{aa = u + v + w, bb = 2 u - v - w},
r1 = Which[aa == bb, AB, aa > bb, AA, bb > aa, BB];
r2 = Which[aa > bb, AA, aa == bb, AB, bb > aa, BB];
r3 = Which[bb > aa, BB, aa > bb, AA, aa == bb, AB];
{aa, bb, r1, r2, r3}]
