There are aspects of each of these within modern American thought.
For example, conservative Americans are more likely to think like the Federalists in economic terms. They worry about the masses getting stirred up by "class warfare" to try to hurt the rich. They feel that this will hurt the country.
On the other hand, conservatives do not trust the federal government. They believe (as the anti-federalists did) that the federal government is far away from the people and is therefore too far out of touch with them.
In this way, there are aspects of both federalist and antifederalist thinking in the US today. Overall, though, I would argue that we are more like the federalists than the anti-federalists because we have accepted a strong federal government and we have accepted for the most part the idea that economic policies that promote capitalism (even if they help the rich) are good for the country as a whole.