I had one experience where I had different tyres front and rear. I had Yokohama A539's all round on the Volvo, and knew how it felt and handled in different conditions. The fronts wore, I replaced them with BF Goodrich's which I was told were a better all round tyre ie better in the wet than the dry. In the dry, the car would 4 wheel drift, in the wet it would understeer with the Yokos all round. With the BF's on the front, in the wet, it was transformed. I could slide the tail at will, and I found this out while going round a roundabout I know well near my house. It caught me unaware first time but the Yokos still being a decent tyre I caught it and starting thinking of the possibilities.... It became great fun!
So if you are used to a car handling a certain way then I would say there is a risk having different fronts and rears. However, with time and you learning how to drive it, there will be changes in handling characteristics on the limit and that is personal preference / choice. One thing NOT to be recommended is different tyres on the same axle, that's just stupid.