Both schools do very well. See the linked payscale rankings for earnings by graduates. Both are ranked top 50:
Both have old established engineering schools with networking that is particularly strong in and around New York City. Both have excellent facilities. Manhattan just opened a new building to facilitate the integration of engineering with other sciences.
Cooper Union is more of a city school, a group of buildings in the East Village. Manhattan has a more traditional campus and college experience in the upscale Fieldstone/Riverdale neighborhood. Each has its own appeal.
For engineering, you really can’t go wrong with either one.