Why A Chebyshev filter trades a flat passband for a steeper transition: it deliberately allows equal-amplitude ripple across the passband (0.1 dB, 0.5 dB, 1 dB designs are common) and in return gets a much sharper cutoff than a Butterworth of the same order. The more ripple you tolerate, the steeper the skirt becomes. That makes it the usual choice when you need to reject a nearby signal, such as harmonic filtering, and a little passband variation does not matter.
Watch out The Butterworth is the opposite design goal: maximally flat, no passband ripple, but a gentler rolloff. The other two choices are contradictory labels, since an op-amp filter is active, not passive.
Chebyshev = Choppy passband, sharp Cutoff. Butterworth = smooth as butter, but slow rolloff.