What's the correct alternative and why?
This isn't a favor to/for me---but to/for you. (Meaning that the one benefited is the other person, not the speaker.)
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To firstly answer your question, the sentence should be as follows:
This isn't a favour for me, but a favour for you.
If you use the alternative:
This isn't a favour to me, but a favour to you.
The person delivering the favour is ambiguous; it could be the speaker or it could be a third party.
If you wish the person deliering the favour to be unambiguously the speaker, you should opt for the first example.
The reason being that the preposition 'for' is explicitly about the receipt of one thing from a given source and, given the other meanings of for, also has a weight of there being a reasoning behind this. As you have already contrasted the pronoun 'me', it would strongly imply the source is also the speaker.
Conversely, the preposition 'to' simply implies a direction of exchange from source to target and hence the person delivering the favour is ambiguous.
I should say, even the first example could be made ambiguous but I think would not normatively be considered so.
"This isn't a favor for me but for you." is the correct version.
While both "for" and "to" can be "used as a function word to indicate purpose, intention, tendency, result, or end" (Merriam Webster), "for" can also be "used as a function word to indicate the object or recipient of a perception, desire, or activity," while "to" cannot.