Basically, the Antifederalists wanted a weaker judiciary while the Federalists were happy enough to have it stronger like it is under the Constitution.
Antifederalists tended to be afraid of excessive power on the part of the federal government. They wanted the state governments to have more power so that the power would not be given to a government that was so far away from them (as things had been under British rule). They felt that the Supreme Court as set out in the Constitution would take too much power to itself. They particularly did not like this because the Supreme Court was to be unelected.
By contrast, the Federalists simply said that people should not worry about judicial tyranny. They said the judiciary would be the "least dangerous branch" because it would not have any power of the "sword" or the "purse."