The differences are there, but they are small.
Let's look at it this way. People in other threads on this forum are getting hot and bothered about a meaningless-in-practical-terms 20% difference in linear resolution between APS-C and micro 4/3 sensors.
Now let's look at what diffraction does: it turns a great lens into a lousy one.
Let's look at a typical example of a good lens,
the current Canon 100/2.8 L macro. The hyperlink takes you to the DP Review test results for this lens on APS-C and FF sensors.
On an APS-C sensor, at its optimum aperture of f/4, this lens resolves about 1600 lp/ph [picture height] on the Canon 50D. At f/8 it's still pretty good, about 1400 lp/ph. At f/16 it's down to about 900 lp/ph. At f/22 it's 750 lp/ph — less than half the peak resolution. At f/32 it's about 500 lp/ph —
less than one third of the starting resolution!
Remember — this is linear resolution. A 3-fold decrease in linear resolution is equivalent to a nine-fold reduction in pixel count: when you stop that macro down to f/32, the 15 megapixel Canon 50D becomes, effectively, a 1.7 megapixel camera. At that point, you might consider switching to your cell phone's camera.
The results on a FF camera, the 5DII, aren't quite as bad (because of its larger pixels), but they are still pretty bad. By f/16 the 5DII is doing no better then the 50D, and by f/32 you might as well be using a small-sensor camera. In fact, if you need a lot of DOF, the small-sensor camera lets you shoot at a wider aperture with a shorter FL lens (for equivalent FOV), and in many cases will deliver overall resolution as good as or better than than the FF system. Hence the spectacular macro results that many have obtained with cameras like the G11.
Do you think that P&S digicams use ND filters instead of apertures smaller than f/8 for no good reason?
As pixels shrink, diffraction becomes a more serious limitation, and pixels are getting smaller across the board, from cell phones to FF DSLRs.
Diffraction matters. It certainly matters as much as using a good lens vs. a mediocre one, or a good film vs. a mediocre one.
If you are not critical (and most of us are not, most of the time), diffraction usually won't matter. On those occasions when you are critical, it will matter, and it will matter a whole lot more than some of the details that many here sweat over.