With my job, I deal with people and their prescription drug plans all the time (Not so much these days, but I worked with them directly for years). People and their atitude towards generic drugs can be incredibly frustrating. Doctors often feed into the parannoia, also. Very often, the active ingredients in the generics aren't just the same kind of drug, but made at the exact same "factory" as the brand name. The only thing that makes them "generic" is that the companies did not create and hold the patent originally, and couldn't start selling the product until they were legally allowed to. Usually the amount of time is 12 years, but there are all sorts of legal games both ways. Sometimes the patent is on the deliuvery method, not the actual drug. So you get some extended release or other more exotic patents.
There is a slim possiblility, of course, that a person could have some kind of a reaction to an inert "filler" material in a generic vs a "brand name" med. But those ingredients are sppecifically chosen to not cause such things. Still, it could happen. But of the 500 or more people that have told me over the years that they can't take generics (it's amazingly common for people to say this), I'd say almost none of them had any legitimate, physical reason to avoid the generics. That's not to say that the effects they experienced were not "real", I'm just saying that they were not due to the generic medicines.
I also used to think that generics may be titrated or measured less strenuously. But, if the FDA is doing it's job (it's not too bad on the world stage, comparatively), this isn't true, either. You should be getting the same amount of the same active ingredient in a generic.
TL:DR version... Just take the generics, if they are available and cheaper.