Are paid options any better? Like the one from Arcgis? Or is google still more accurate?
What regions? I work in GIS and have tried Nominatim in several projects, and it always ends up being so error prone we have to abandon it.
But that's for cities, in anything rural/mountain Nominatim takes the lead. Google seems not to care for addresses that aren't residential or a business. Arguably most geocoding uses are shipping things and business info, so most commercial efforts go that way.
Then some areas are just abandoned by Google. When I lived in Ukraine I tested some addresses and about 1/10 of the requests didn't work or were just wrong, and that's leaving aside the fact that it always showed 01001 as postal code on every reverse geocoding within Kiev city that I threw at it. The only information that was reliable was business data, and mostly because of businesses themselves updating it. The transliteration was software based and often wrong. Russia and Central Asia are also a big mess, though big cities tend to have OK data, but my feeling is that Google dropped the ball against Yandex and they just don't care anymore; not their turf.
It might have changed for Ukraine since, since there has been a push to drive away all Russian techs, maybe someone can shed some light on the subject.