An OIII filter will only work well on nebula which transmit strongly in the OIII band, ie one which mostly contains doubley ionised Oxygen, such as the Veil nebula. According to the link below;
http://www.astrobuysell.com/paul/filters.htm
there are lots of nebula strong in OIII, particularly panetary nebula and as it's a line filter, it will make the background very dark.
However, you are missing out on all the other bands, such as the very common Ha. A UHC filter will allow you to see all the major bands, whilst blocking out unwanted light, but it won't block out as much as the OIII would as its pass bands are wider.
That's why narrow band imagers using line filters get excellent images, as they make the background so dark, but multiple filters are combined in the image processing, so you can capture all the emission bands, of course you can't do this with your eyeball, so you either need to capture all of them using a UHC and risk a brighter back ground or see one emission at once using an OIII or Ha filter, with a darker back ground.
The filters are so narrow though, that they are generally best with large aperture scopes for visual. (Imaging is another matter).
Their performance will also depend on whether you have good or bad light pollution in the first place.
Regarding using a filter on galaxies, I don't think it's as clear cut as you say in a light polluted area anyway. I think a UHC filter will still darken the background light pollution and allow most of the light from the stars to pass through, making it appear better.