Each tire type has different rubber, and hence different friction
characteristics. These days, I don't think you could find a non-radial
tire less than 25 years old, so that's not a problem (radial/bias belt
tire mixes can be lethal), but the difference in adhesion to the road
can be quite dramatic. Having one tire track better than the other
leads to unstable handling, and in an emergency, you can loose control.
The best possible "mismatch" is for one pair on the front and one pair
on the rear.
That said, I've driven any number of cars with mismatched tires, but
believe me, a full set makes a big difference! It really is best to
stick with all four the same make and similar age.
peter