A few things:

Privacy-wise, no, neither one of those Microsoft services are good alternatives to Google. Microsoft is just another flavor of an enormous corporation milking your personal information for profit. If that’s your number one concern and decision maker, then stop here and consider something else. I don’t think there’s anything as polished as Google drive, but some actually private services are pretty good. Proton Drive is usually the most recommended. I use filen.io, it is very cheap, encrypted and works pretty well. Skiff Drive is also very good, they don’t have as many options for drive space but they have a suite with email, calendar, drive storage and documents (not like Office mind you, a more simple kind, like formatted notes), all encrypted. If you want something that allows collaboration and is well integrated skiff is probably the best option.

Now if you don’t want the highest privacy but just something that isn’t google, well I have used OneDrive and it has never worked well for me. The short period of time that I decided to use it on windows it broke constantly, I had to log out and in a few times because out of nowhere it stopped working. It didn’t delete files or resynced files that I had deleted in some other device. Maybe those issues have been fixed since, I don’t know. But even if we completely ignored the privacy aspect, I would not recommend OneDrive to anyone.

Maybe the biggest issue is the office suite. If you need the advanced features of Microsoft Office, there’s simply nothing that can replace it. If you don’t, then a local alternative may work for you, like LibreOffice or Onlyoffice. You can also use office online, it’s simple but it is maybe the second best option after full desktop office. But again, you are relying on OneDrive even a little. What I do when I need it is I download the file I need to work from my filen drive, upload it to office online, work with it, download when I’m done and move it to my cloud. It’s a bit cumbersome but I’ve never had any problems. But mostly I use Onlyoffice on my desktop.

None of the private alternatives are as easy and comfortable as Google or even Microsoft services, that’s for sure, so whatever route you end up following make sure to try first so that you can see what to expect and what is the best for you.

In the road to privacy I’ve found that being an absolutist of the ‘ditch everything right now and move to Foss’ kind is not a sustainable way for most people and only leads to them going back to the old ways. Small careful steps one at the time is an option that almost anyone can get used to and work long term.

I recommend you to check privacyguides.org for more explanations and good alternatives.

Thanks for the long read and good luck.