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In my opinion, "appropriate" has attached to it a "correctness", a "rightness", that isn't found when using suitable. The following sentence points this out:
"That high-skirt is suitable for the dance video, but inappropriate for you to wear". Here, you can't really say that the dress is unsuitable for her/him to wear because its suitability is relative to the occasion, and this occasion demands that sort of clothing. However, regardless of the occasion, it is inappropriate to wear the skirt in the sense that there would be a loss of "correctness", a depreciation in respectable value almost.
This is my attempt at lucidly explaining Whistleblower's post, though adding perhaps a bit extra.