Negative ions rid the air of pollen, dust, etc.: stuff you can see under a microscope. Ozone cannot. Negative ions also can improve mood. Ozone cannot do that, either.
Ozone gets rid of odors, pollutants, etc.; stuff at the molecular level (although negative ions can get rid of some odors, too.)
Myth: Negative ions are nothing more than ordinary static electricity.
Fact: That is a falsehood. Is there static electricity near waterfalls or other areas where negative ions are naturally generated? Of course not. Although some ionizers can induce a 'static' charge on nearby objects under certain conditions, negative ions flow through the air like electricity through a semiconductor.

Myth: Negative ions can go through walls.
Fact: No way. Neither can ozone, although ozone (if present) can go through heating and cooling ductwork. Negative ions generally cannot; they are attracted to the filter, air conditioner evaporator coil (A-coil), and very few emerge at furnace or air conditioning vents. The exception is properly designed and placed UV lamps, although they do not put as many negative ions into the room as a good room ionizer.
Myth: Too high a level of negative ions in the room is bad for you.
Fact: Negative ions have not been found to be harmful even in very high concentrations. Just the opposite has been found the case. In fact, there are patents using high-density negative ions to treat depression.

Myth: Ozone is ALWAYS a bad thing.
Fact: While ozone in extremely high concentrations is a toxic gas, if the ozone level is properly selected, the ozone and the pollutants/odors in the air CANCEL EACH OTHER. Overlooking this fact is the cause of the ozone controversy we sometimes see. What is more, a little ozone is often far preferable to the toxic gases and pollutants it can eliminate from the air we breathe.
http://www.bright.net/~comtech/ions_ozone_myths_facts.html