Most mechanics and tire shops, I think, recommend that all 4 tires be of the same age and model. Of course they have a vested interest in selling tires. I would be reluctant to have different tires on the same axle. 2 of the same on one axle is OK though. I have been driving my personal car with Michelins on the rear and Continentals on the front for nearly 2 years without problem. The insurance company really should have paid to replace both tires on the axle where the tire was damaged. However if you have already accepted the one replacement tire, it probably would be difficult to go back and argue for the other.
I would agree with Dave though. In normal driving you most likely wont feel any problem. However, there might be some loss of responsiveness in an emergency maneuver or in rainy of snowy conditions.