Had to do that once, land on the remaining runway.
152 had a magneto go out of timing, internal gear had sheared off.
About a 100' in the air on a 5000' runway.
Lowered the nose put full flap down, it takes a fraction of a second to reach the flap lever. Don't recall how far they made it dowbn before we touched down. Without flap I would have gone off the end no doubt.
Me thinks it would have to do with your reaction time also.
If you are slow in getting the nose down the speed will have deteriorated so much already that pushing the nose down to recover the speed will have the same effect as application of flaps, loss of excess altitude.
Too slow and flaps down will not (depending on altitude) give you sufficient height to recover energy to flare, very heavy landing with excessive rate of descent.
Landing distances in the POH always state the conditions, eg full flap threshold speed 58 kts etc etc.
So to me flaps down would always seem to be the better option, unless you're too slow.