Can high-end brake pads/shoes be 'too good' for my car?

I have a 2002 Toyota Corolla. I've never had problems with the braking system at all. I had the brake pads and shoes replaced at a Firestone which used OEM parts. No problems. My dad, upon hearing that I'd had a real mechanic install brakes for what he considered a huge amount decided that he would have his mechanic install 'the best' pads/shoes. Now, they make an aweful squealing noise, usually when I first start the car (e.g., they get quite once they get hot) or when it's wet outside (especially when it's wet). I just want to note that I have no problems with actual stopping ability -- the car is able to brake normally save for the noise.

I've had the mechanic look at it twice and both times he said there's nothing wrong with them. I've looked at them myself and haven't seen anything out of the ordinary (no abnormal wear and tear, no glazing, etc.).

Is it possible that the 'top of the line pads' are just too high-end for my economy car? Usually cars that make this kind of noise are in poor condition but mine is not -- it's actually in very good shape. Frankly, it's humiliating when I brake and it sounds like my car is about to fall apart and I'm wondering if replacing the brakes with OEM pads/shoes will resolve my problem...

The mechanic did a lousy job of installing the pads. You can take the pads our and have them reinstalled. This time have them put a bead of silicone sealant on the back of the pads and make sure that all the clips are good and tight.

Tell you dad that his mechanic gets in too much of a hurry and does not spend enough time on the details.

Oh, the pads are not "too good" for the car. Always get good, high quality pads or they will not last. My wife had cheep pads put on her car and they lasted less than 30K miles. My truck, on the other hand has over 75K on the pads on it and are still OK. I will replace them this summer anyway because I need to repack the wheel bearings and replace the wheel bearing seals.