I think it depends on ease of implementation.For example, a particular configuration may be more easy to implement in a Switched capacitor implementation whereas something else may be useful for digital filter implementation.I am not an expert in either, so wouldnt comment further,
if a1 and b1 in the 2nd plot are the same, the two configurations are the same. if not so, a1 in the 2nd plot can be changed based on the input signal, this is its flexibility.