Its not so much as it reduces the quality but that it potentially can change the sound, especially when making large corrections. There are two basic kinds of EQ: IIR (Infinite Impulse Response) which would be an analog EQ or minimum latency EQ. The other basic type is FIR (Finite Impulse Response) which is a phase linear EQ. Both types introduce distortion into the sound. IIR causes phase distortion which becomes more audible the more severe the setting. FIR delays all the bands equally so it does not have a phase problem, but it does introduce a pre-ring, which can be more audible. In general it is usually more transparent to cut than to boost. The narrower the Q, or band, the more audible the change can be when boosting, but you can often cut a problem frequency without changing the sound too much.
As for the difference in quality between hardware and software, that all depends on the hardware and the software. If you are meaning is it better to use the EQ that may be included on your amp or the EQ in something like Foobar, I could not say for sure. If you mean pro audio application hardware and digital audio workstation software then both are of very high quality, and it depends on the result you are trying to achieve.
I would say mess with both and find the result you want. Try cutting areas that seem like they may be getting in the way to see if it will open up the sound. Start with a broad cut, then narrow it in until you hear the result you are looking for.