In general, the person with the $25,000 in income is likely to make out better when claiming the child as they would claim head of household, get the child tax credit and potentially the Earned Income Tax Credit.
The person with the higher income would still claim Head of Household and get the Child Tax Credit, but not the earned income credit.
Thing is, the rules for claiming Head of Household, is that you cannot claim head of household if you do not provide more than half the support for maintaining the household. So since you live together, and they provide over half the support, your benefits would be less than if you lived alone with just your child.
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