QuasarMX supports many different back ends. It is using Qt Mobility on the N9 because this back end integrates best with the media stack and has the lowest power consumption.
Other back ends are Phonon, GStreamer and MPlayer. Phonon or GStreamer are probably what the other players use in order to get the EQ functionality. Most of the EQ filters do not use the DSP and as a matter of fact will drain the battery because the CPU has to do all the hard work.
I hope to have a better solution ready but it might take some time. I am brutally honest here, the EQ is low on my short-term to-do list. There are more pressing issues right now.

To answer your question: No, the player does not have any effect on the sound quality.