John Atkinson typically does nice thorough measurements of reconstruction filter responses in Stereophile’s DAC reviews. Here is a link to a high end Gryphon player measurements, showing the differences in the various filters.
https://www.stereophile.com/content/gryphon-ethos-cd-player-da-processor-measurements
In my understanding a “fast” filter has a very steep low pass transition. Sometimes called a “brick wall” filter with virtually zero signal above 22.05 kHz (for 44.1 kHz sample rate). This allows less roll-off below 20 kHz.
Impulse response is one of the characteristics of different filters. Typically a “fast” filter will have significant pre-ringing which might sound unnatural.
On the good side a “fast” filter generally reduces the chances of aliased artifacts being artificially created above the Nyquist Frequency (22.05 kHz for redbook).
In my experience, some DACs have obvious sonic differences between their filter choices. Some not so much.