Starting in the tax year of 2008, each personal exemption that you claim gives you a deduction of $3,500 against your taxable income. The person with the income of $45,000 will be in a higher tax bracket than the person with the income of $20,000, so there will be a bigger tax advantage if the person with the higher income can take the deduction.
If two individuals were both in the same tax bracket, there would be no advantage from one over the other claiming the deduction.
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