Basically, what a program like Ozone does is the same thing that’s done at the “mastering” stage of production of a record. i.e., when a mix engineer mixes a track s/he gets the balance right between the musical elements (volume-wise and tone-wise, i.e. bassy or trebly) like bass, drums, guitar, voice, etc. That’s the mix. And then the final stereo mix is put through processes (overall eq, compression, limiting, other kinds of enhancers) that further enhance the mix as a whole - and that’s mastering.
In the days of vinyl, mastering used to be a highly specialised, somewhat voodoo process, because the mastering engineer’s job was not only to make the final mix sound as good as possible, but sound good on vinyl, a mechanical, quirky transcription process - and not only that, but to master the track so it sounded good on vinyl when played on radio (which until FM came along, was a very poor quality transcription process).
Nowadays, software mastering tools (like Ozone) are part of most music production packages, and because digital doesn’t have the same constraints as vinyl, you can pretty much master it how you like it to sound. (Which has its own downside - at the moment, there’s hot debate about “hard limiting”, which is something that makes the final mastered mix sound as loud as possible, there’s been something of a volume “arms race” in recent years, which has meant that modern masters tend to be “flat”, cranked up to the max, without much dynamics - also you can hear them “pumping”. Now a certain amount of “pumping” is desirable, especially in pop, rock and dance, and is indeed what in other contexts is called “phat”, but when it’s overdone it sounds overbearing and oddly lifeless and lacking in “transients”, which are the short, sharp, high volume “crack” at the very beginning of percussions sounds, snare drums, even the hard picky sound of guitar notes.)
So, if you run a track that’s already been heavily mastered through something like Ozone on a high quality audio system, it tends to sound overdone, but if your audio hardware is lower grade, it might sound ok - i.e. just like the old days when records had to be made to sound “big” when played on tinny radios, it might actually enhance the music a bit more so that it compensates for (i.e. sort of “punches through”) the lack of quality in the hardware.
At any rate, with most people listening to their music on the appalling mp3 format these days, most of these arcane audio matters are moot :)
As a general point, with electronic music or dance based music, lots of mastering and pumpage generally sounds good on a home audio system, whereas with acoustic-instrument or heavily vocal-based music with lots of dynamics and subtlety, its bad and obliterates a lot of the subtlety and sounds over-pumped.