I think it's very, very hard to say.
The only more correct numbers I know of are those from Karen Wynn Fonstad's Atlas of Middle-earth, since they are based on certain quotes in the books. However clear numbers do not exist.
For example, it seems pretty clear that much more Men served Sauron, for example the slaves mentioned in LotR that work near the Sea of Nurnen...so exact numbers can't be given in this case
With the good guys it might be easier, but again only speculative numbers based on the books.
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