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The paper filter will also have a large effect on the flavor of the coffee produced. Paper filters are designed to remove oils from coffee, but the oils removed by the paper filter can be a substantial source of flavor for the coffee produced, as many of the flavor compounds in coffee are fat-soluble.
Coffee produced with a paper filter will have less sediment, fewer oils and, in the opinion of many metal-filtered enthusiasts (myself included), a more even, less robust flavor. That shouldn't be regarded as an inherent downside, however, as many people prefer the flavor of paper-filtered coffee, finding the mellower profile and lack of sediment/oilyness preferable. Crema is more pronounced in metal-filtered than in paper-filtered coffee.