I don't think you can reduce things to "perform better" or "perform worse". For profit ventures can be many things very well. But one also has to consider what they perform.

For profit education is great for giving a single individual specific skills they need that will make them money.

For profit education is unlikely to be interested in giving a person a "wide liberal arts background". And the thing about a wide background is that isn't worth much to the individual in terms of money. They might look back on their lives as having been richer for it or they might not. But giving a person a wider background is worth more to society as a whole, in everything from life being more interesting to politics being less polarized.