I know that the money "produced" from the federal reserve system is fiat money, but does that apply more to the dollar bills as opposed to coins? Is it worth it more to have coins than paper money then? Is there a catch with the coins though?
Well, yes and no:
1) Fiat currency derives it's value from public confidence, which in turn is derived from the government's promise that it will suffice for "all debts, public and private."
2) But when inflation reduces this purchasing power (i.e., it takes more of the dollars to satisfy the debt), possible completely, then the money is only worth the paper it is printed on.
3) With coins, they will be affected in the same way (i.e., they will lose their purchasing power just as paper currency does; after all, they are but denominations of these same paper bills), however unlike paper, they will never be worth zero, because the base metals of which they are themselves comprised still have market value.
4) In some cases the "melt value" of the metal exceeds the "face value" of the coin (such as is currently the cased with nickels and pre-1982 copper pennies).
5) This explains why some people have begun hoarding these coins (i.e., They anticipate greater value once the government is forced to change the metal content of these coins, just as they did with pre-1964 dimes/quarters, because when the melt value exceeds the face value, the mint produces them at a net loss.
6) Changing the content of the nickel has already been proposed, and once they do so, their value as collectibles will further increase their melt value and/or numismatic value.
7) In other cases, the face value far exceeds the melt value of the coins (e.g., dimes and quarters).
8) So a long-winded way of saying inflation will affect both Federal Reserve Notes and coins, though differently (and because of their content, not their origin).