My own experience clashes somewhat with the majority view here - my view is that smaller wheels eg 16" does not give a harsher ride than 700c wheels. In fact my experience is to the contrary - big-wheeled bikes I have ridden were harsher over those sharp bumps such as the edge of pavements.
Due to the frequently expressed majority view here, I have begun to waver in my opinion, that perhaps my riding style has imperceptibly changed such that despite smaller wheels' alleged harshness, my style renders the effect of smaller wheels irrelevant. Such a riding style might be to slightly lift myself off the saddle a very small amount on encountering a rising bump, as well as giving the handlebars a small jerk to lift the front wheel over such a bump.
Anyway, I did a mathematical analysis and some simulations of the axle displacement when riding over a square bump, the worst case. The bump I investigated is a square edge 25mm rise and later a fall (opposite sequence of a flat pothole) at a speed of about 20km/h. The findings were very interesting.
I compared a 16" 305x50 wheel with a 700c 622x28 wheel. The 16" 305 wheel is less than half the diameter of the 700c wheel so any effect would be like a worst case. Adding a tyre changes the ratio quite a bit; the 305 wheel got a 50mm tyre (eg Big Apple) and the 700c wheel got a 28mm tyre. So the effective radius of the 16" wheel was 202.5mm and that of the 700c wheel was 339mm.
I looked at the horizontal distance between each axle and the front edge of the bump as the wheel first touches the edge. The ratio between the 2 cases is 1.31 (700c wheel being the largest).
First of all, the result with extremely hard pumped tyres. The vertical acceleration ratio between the 2 cases was also 1.31. Makes sense of course. The 16" wheel suffered the highest vertical acceleration as expected.
Then I dropped the pressure on the 16" wheel by that same ratio, 1.31. So if the 700c wheel was 100psi, the 16" wheel was 76psi. For this, the 2 cases' vertical acceleration amplitude was essentially equal albeit with different shapes. Furthermore, if the pressure of the Big Apple is dropped to say 40psi, the 16" wheel acceleration drops to 60% of the 700c wheel's. The 16" wheel does experience a much bigger rebounce, though, but still very small in the grand scale of things - only about 2mm. Such rebounce would be completely obscured by something like seatpost flex.
So as far as I can see, here is proof: Smaller wheels with everything else being the same, are harsher, but with tyres pumped to realistic pressures, the situation is much the same or even reversed.