The difference could be up to $1500 per child.
A child must have a social security number to be eligible for the Child Tax Credit or Additional Child Tax Credit per IRS instructions. The Child Tax Credit is a $2000 non-refundable credit. That means the credit amount cannot exceed your tax bill. However, if your tax bill is only 600 you would get $600 for the Child Tax Credit, but then $1400 for the additional Child Tax Credit to make up the difference.
Here is a link with more information on the Child Tax Credit.
With an ITIN you get the $500 refundable credit for other dependents.
See the paragraph "How do I get a TIN" in this link.
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