When you reach this volume of data, especially when they are on two different servers (hence... a network of some kind will now be involved ...), you're simply going to have to devise some strategy that will enable you to “divide and conquer.”

There are various possibilities to consider, depending on exactly what kind of comparisons you want to make.   For example, I once worked on a similar task where we pulled row-counts and MD5-sums of blocks of records, then compared those results, gradually zeroing-in on the differences.   (These queries focused on just one server at a time.)