Would the federalist or anti-federalist be more upset to see a president challenging the authority of congressional statutes?
Actually, this does not really fit very well in the federalist vs. anti-federalist debate. Neither side would care very much about this. But if you have to pick, the anti-federalists would be more upset. Here's why:
The real split between these two ideologies was over who should have more power -- the states or the federal government. The federalists wanted the federal government to have a lot of power, the anti-federalists wanted power to remain with the states. Given that, a power struggle within the federal government would not matter that much to them.
However, the anti-federalists were very concerned that the federal government would take away people's rights. They would probably have been more worried by a strong president than by a strong Congress because they would think a strong president would be too likely to try to become a king.
In general, an anti-federalist, simply because they were more suspicious of the role and power of President from the beginning. They believed more power should rest with the individual states, which meant Congress would have the upper hand in decision making power.
Later, after 1801 and John Adams "midnight judge" appointments, they would be worried the Supreme Court challenging congressional statutes as well, since Adams' judges tended to side with the power of the federal government on most issues.
On the other hand, the anti-federalists biggest concern of the time may well have been the Constitution being undermined by a President as opposed to just individual Congressional-Presidential showdowns.