In general slow filters are less likely to introduce artifacts than fast filters but introduce a longer group delay (the time for the signal to propagate through the filter). Group delay is usually not important unless you require the audio to be synchronized to some other sensory stimulus (e.g. video).
Linear phase filters prioritize the preservation of phase relationships between different frequency components at the potential expense of the amplitude relationship whilst minimum phase filters allow the phase relationships between different frequency components to change in order to best preserve the amplitude relationships.
Having said this, the audible effects of the different filters provided in the FIIO are likely be subtle even to the extent that the differences can be very hard (or impossible) to hear.
The amplitude artifacts introduced by linear phase filters are likely to occur at high frequencies - quite likely above the audible frequency limit for most people. The phase relationship artifacts introduced by minimum phase filters are usually not audible but, in some specific circumstances, could conceivably affect sound stage perception.
In conclusion, don’t worry about it if you can’t hear the difference.
I did some more listening, switching back and forth between the different filters on the FiiO K11.
For me, Filter #1 (Slow Roll-Off / Slow Linear Phase) sounds the most natural with the DT 880 (600 Ω) .
It keeps the transients clean but avoids the slightly edgy treble that I sometimes hear with the faster filters.
The DT 880 is very revealing in the upper range, so even subtle changes in phase or pre-ringing seem noticeable — cymbals and vocals just feel a bit more “free” and relaxed with the slow filter.
The stereo image also stays stable and focused.
In the end it’s subtle, but this setting feels the most balanced and least “processed” to my ears, especially for long listening sessions.