The best person I know to answer this question is Glen C. Hopefully he will respond with a more comprehesive reply than mine.
The only use for an OIII filter is on planetary nebs, and is most useful for faint planetary nebs. It does bring out detail in the eta carina nebula, but almost all bright emission nebula respond much better to a UHC filter.
The UHC filters have wider bandwidth transmission pass than the OIII, so some faint extended objects, like Barnards Loop (naked i) which are virtually invisible in an OIII while explode with detail in a UHC. The UHC filter is probably your first and most useful filter to buy. As the UHC also transmitts OIII, they are also useful for planetary nebs. If you don't believe me, try it on planetary neb NGC 2438 on the northern edge of M46. I can't discern any difference between an OIII and UHC.
M42 the Orion nebula has a high enough surface brightness that filters don't really matter, but a UHC will bring out some of the fainter wisps.
What objects /nebula etc which respond to a UHC filter? M8, M16, M17, ngc6888 crescent, Rosette, Tarantula, Veil, California neb, Vela SNR, the various emission nebs like ngc2626 in Vela, NGC2023 in Orion, bright RCW objects (RCW86, 108). Basically, all bright emission nebula. I have found the improvement stunning, and I can thank Glen C for recommending them to me.
From areas with more skyglow, the OIII would probably be the filter of choice, but from dark skies, the UHC is it.
I do not have any experience with the sirus nebula filter. It is claimed that the filters have a wider transmission than the narrowband O-III but not as wide as the UHC. With a large aperature scope and dark skies they probably perfrom similarily to OIII filters IMO.
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