Is problem finely detailed rare coin better than a no detail Problem free coin?

A one year type quarter. So She has the mumps and graffiti which are nicely described as "Counter Stamped". Why not American Chop marks? I think that the "problem free" coins at some point will not be the be-all-and-end-all of collecting. In this case the coin pictured was in an auction with another that was problem free but with "About Good" grade (rubbed smooth) and sold for thousands more. I lost this coin in the Long Beach show a couple of years ago and now the price was less (because it is not a problem free coin). With only a a couple hundred of these one year coins in existence I would rather have a problem coin with fine "details" rather than a problem free coin with no "details". I could be all wrong...

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