I had one of those fitted to the bathroom in my previous house - it
seemed to be ok, other than it was harder to keep the 'button' clean
compared to a traditional handle. The other advantage it had was that
by holding the button down until the flush finished you got a 'half'
flush - usefull for flushing away non-bodily waste and not having to
waste a full cistern of water.

As others have said - not as obvious when you were in an overflow
situation, but then again, you don't end up with dribbling water
pouring out the external overflow, which as such a low flow usually
ends up leaving a nice water mark down the exterior wall.