I think that slavery generally disappeared in the North (was legislated out of existence either suddenly or gradually) in the period before 1800, mostly due to moral arguments.

The free labor vs slavery discussion came later.

Before 1800, the number of wage laborers in the North was small. The bulk of the population were farmers (only 7% of the population lived in cities with more than 2,500 people in the 1790s).

Farms in the North were generally family farms. Farms in the South that employed many slaves were large plantations. These were very dissimilar, and the economic argument did not often arise.

As the North became more industrialized, and a higher percent of the population became wage laborers, then this became a topic.

The South often argued that the new Northern working class were exploited and downtrodden wage slaves who were actually worse off than Southern plantation slaves.

The north had a variety of free labor arguments summarized as:

Free labor will work hard to get more money and promotions and better themselves. Slave labor will only work the minimum they need to to avoid the lash.

Free labor can move from an inefficient or bad employer to an efficient or good employer who will reward good workers with higher pay. Slaves cannot. Thus the free labor society will use its resources more efficiently and become more productive.

Free labor is better for enterprise and innovation, as the free laborer can learn, and save his money, and then strike out on his own with new ideas and innovations. The slave cannot.

Abraham Lincoln put the whole free labor concept into political rhetoric when he said, “I am not ashamed to confess that 25 years ago I was a hired laborer, mauling rails, at work on a flat-boat—just what might happen to any poor man’s son!” and went on to say that his belief that he could better his condition, the same belief that any free man could have, was what gave him hope.

He categorized the South as lacking hope, energy, and progress, due to the institution of slavery.

https://www.binghamton.edu/history/resources/journal-of-history/lincoln.html

Of course, generally the two camps were talking about different belief systems, and talking past each other, rather than doing anything resembling economic analysis.

I don't think anyone knows the relative efficiency of free labor vs. slave labor at the time of the Civil War. Large Plantations were probably more efficient than small family farms (witness the growth of large agri businesses today). The North, however, did have a much more dynamic, innovative and industrializing economy than the South, and was growing faster.

On your question about how could paying someone to do work be a better deal than having slaves do it for nothing, you need to realize that slaves did not come free. The slave owner needed to buy the slave (over $1000 for a prime field hand just before the Civil War) and feed and maintain the slave, whereas the employer did not need to make an up-front investment, just pay wages for work.

So, paid workers were not necessarily more expensive.