When you state that the click appears when switching between 16 and 24bit music files, I immediately think that what you really do is to switch between music of different sample rate (44.1kHz/16bit to 192kHz/24bit, for example). Ripped CDs are 44.1kHz/16bit, while most high-res audio files are at sample rates of 48,88.2,96,176.4,192kHz and almost invariably 24 bit (although I have seen the combination 44.1kHz/24bit files also).
If you play back sending the audio file's original sample rate, the DAC has to switch to the new sample rate before playing. Some DACs will spend a bit of time locking into the new sample rate, and produce an audible pop or click once done. My Lynx Aurora does this, which was a bit annoying. It has made me set it on fixed 96kHz and JRiver is set to resample all sources to 96kHz. Problem solved for me.
My guess is that this is the cause of your reasonbly loud glitching noise.
By the way: 16 and 24bit are not bit rates, but bit depths in your audio file. The sample rate is the digital resolution in time, while the bit depth is the resolution in volume. The bit rate is the number of bits pr second transferred in your audio path while playing.