Although it is possible that the largest stack is selected to be moved, it is statistically improbable, and regardless, totally random. Aside from the fact that more chips are at the newly-filled table, that is offset by 1) having no dominating stack at the now-shorter table, and 2) potentially having multiple large stacks at the other table. So it's certainly debatable which table's players -- if either -- have an advantage.
My personal opinion is that stack size (or the resulting table-chips counts) should have no bearing on table-balancing moves, and the commonly accepted tournament rules agree.
Standard tournament rules also call for a full random seating redraw when breaking down to three, two, and the final table.... with zero consideration for stack sizes. Some large home games do this, others do not.