90% of the time, you're not going to notice are you? but in a 4wd car, then at the point that you're starting to lose traction, you ideally want all four tyres to have the same degree of grip. If you have different tyres on front and rear and they have different grip characteristics, you're could get front and rear losing traction at a different time to the other - which isn't ideal for getting the best traction.
Even on a two wheel drive car, when you're cornering, the suspension is designed to be "balanced" assuming the grip from all four wheels is the same.
If you have different tyres with different grip levels on front & back, then when cornering near the grip limit, you could get the front or rear breaking away, in a way that is different to the safe, neutral way that was designed in by the suspension designers- you could get unexpected understeer or oversteer if the front or rear breaks away before the other end.....
I had a 2wd Alfa 156 that felt really awful cornering on roundabouts even at reasonable speeds, when I bought it and it had two different types of tyre on it. As soon as I fitted all four of the same tyres, it felt great again - just like my previous 156....
So you're really not going to notice much until you get near the grip limit and then the issue is that because you can't predict how the two different tyres will react in the same extreme circumstances, you can't predict how the car will react...
Having completed my rant - I'm sure that nearly half the cars in the country will have a mix of tyres and I'm sure most people survive - but personally, I prefer to know I'm going to get the same balanced grip from each corner....