I read that modern full frame cameras 'expose' or 'reveal' the flaws in lesser lenses more than crop cameras. To me this doesn't make sense save a couple caveats.
There is a good reason that it does not make sense to you because it is false, in the majority of the cases.
First, we are talking about EF lenses only. In the center, FF sensors enlarge the image 1.6x less. If that was the only factor, then FF would resolve 60% more in the center. But there is also pixel density/AA filter. To make it simple, assume the same pixel count. Then the FF advantage in the center, same lens, same f-stop, would be from 0% (ideal lens) to 60% (very soft one). In reality, it goes up to 40%, depending on the lens and how you measure it.
The meaningful comparison however is for equivalent f-stops and equivalent FL's (same AOV). Then FF has even greater advantage for soft lenses, like 85/2 vs 50/1.2, where FF resolves even more than 60% more. When you stop well, then diffraction is the real limit, and then asymptotically, FF and crop have the same resolution.
In the borders, FF "reveals" the flows of the lens in the corners. Well, it still enlarges them 1.6x less; and for equivalent lenses, you have to stop the FF more. Then (depending on the lens), most of the times, you get a better resolution in the borders as well. A notable exception usually cited is the 17-40 in the borders but TDP shows otherwise (the lens at 17mm is focused there too close, BTW). Still, exceptions exists, I guess.
It only makes sense to me to compare not the same lens on FF vs. crop but the lens that you may use on FF vs. the one you may use on crop. Then the 17-40 in the borders is better than the 10-22 on the wide end, according to the TDP crops (again, focused too close).
Here is a graph of the resolution (in the old units DXO used until recently, MTF-20), in the center, 50/1.4 on the 7D, vs. the 85/.8 on the 5D2, in equivalent
f-stops. I was planning to draw a similar graph for the border performance but DXO decided to hide their data.