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Usually, the family comes out better if the higher income parents claim the child. He can usually claim Head of Household, if he has a dependent. The lower income parent usually cannot.
But the only way to be sure which way is best* is to do comparative returns prior to making a decision. This tool is useful for that purpose: <a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1">https://turbotax.intuit.com/tax-to...>

*It's possible for the lower income parent to get a bigger Earned Income Credit (EIC) than the higher income parent and this can, sometimes, make the difference.