We have a classical C-S(client-server) architecture, i.e. a mobile app and a business server. We have our own account system (not using 3rd party accounts such as G
The resource owner flow is considered unsafe when used with 3rd party authentication, for example your mobile app is trying to access a file in the user's Dropbox or a Gmail's email. If you own all the parts of the system account system, resources and the app your should be safe with resource owner password flow.
It is a much simpler flow, however it has some drawbacks. Like you won't be able to federate with other 3rd party or enterprise systems, and you can't benefit from a single sign on. If neither of those apply to you go ahead and use resource owner password flow.
You can find a good treatment on the subject here : https://auth0.com/blog/oauth-2-best-practices-for-native-apps/