I would ask to see the invoice from this more competent person and ask if you can contact him to find out what was wrong. Just say you want to approach this as a learning experience. If nothing comes of this ask him what he thinks your service was worth and accept whatever he wants to pay you and write off the rest. Just inform him if he undervalues your work, you won't work for him again, you don't work for peanuts.
I once had a guy who only wanted to pay for the printing and not design, treated him as above. When he came back for changes I told him as our artwork was worthless to him we had deleted it. He went white and we never saw him again but was not happy if you let customers walk over you they will. Good luck with this dealing with unreasonable customers is hard, so look for reasonable ones.
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