First of all - I don't have information about the whole picture, but even based on the information you have provided so far, I would go for separate table. It's the proper DB design.
As to the performance/cost of INSERT vs. UPDATE (I assume you will either insert new records or update existing by concatenating new values to existing string, right?) - it's really a tricky question and depends on many factors, so I definitely cannot give a definitive answer. Probably you can run comparison test. I would expect that inserts in separate table would be less CPU intensive, though.
As to the performance/cost of INSERT vs. UPDATE (I assume you will either insert new records or update existing by concatenating new values to existing string, right?) - it's really a tricky question and depends on many factors, so I definitely cannot give a definitive answer. Probably you can run comparison test. I would expect that inserts in separate table would be less CPU intensive, though.
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How to Ask Questions The Smart Way: link and another link
Create MCV example
Debug small programs