FSL’s temporal filter is not well suited for anything other than high pass filtering. IIRC, it is implemented as a gaussian filter.
The bandpass filter code uses FFT based filtering. While the filter is ideal in this case, since it is constructed in the frequency domain, the FFT transformation is not. Since a compact representation in the Fourier domain can only come from an infinite time series signal.
The easiest way to empirically test the code, would be to create a white noise time series, run it through both approaches and look at the power spectrum or even the spectrum or spectrogram of the output.