There will be no loss over the HDMI cable, but the monitor might make a difference in a number of ways.
The signal will take a path like this PS4 (digital source) > Monitor (still unmodified digital) > DAC (inside monitor, conversion to analogue) > Amp (may or may not be inside monitor).
The DAC, amplifier and supporting circuitry can have an impact on sound quality. If the monitor output claims to be 'line out' then it will probably be a non-amplified output with no volume control. However if it's a headphone port and has a volume control, it probably has an internal amp.
Line-out with just the DAC would probably be the best option for self-amplified PC speakers, and the setup I suspect your monitor will use.
TBH I'm not too sure what the DAC quality would be like on monitors but unless you're after a fairly expensive audio setup it should be fine. If not, it looks like another option would be to utilise the optical out port on the PS4.