How to ensure the two schematic diagrams are equivalent?
Yes. You print out the two schematics and then check each component and connection manually. As you have checked each one highlight it with a yellow marker. When you get all done the whole schematic should be all yellow. 

Along the way keep a pink highlighter handy. Whenever you find a mistake or mismatch use that color to highlight and this will be your reference for all the mistakes when it comes time to update the schematic.