I'd say Copper is strictly better than Curse.
Nuh uh. If your opponent plays a Mountebank, you'd rather have a curse in hand so you can discard it and avoid getting that nasty copper.
If you play an Ambassador you'd rather have a curse in hand so you can give that to your opponents.
If you play an Adventurer, you'd rather hit a curse then a copper so it will keep looking for better treasure.
If you play a Venture, you'd rather hit a curse then a copper so it will keep looking for better treasure.
If you play a Farming Village, you'd rather hit a curse then a copper so it will keep looking for better treasure and actions.
If you play a Masquerade, you'd rather have a curse in hand so you can give it to the person on your left.
If your opponent plays a Tribute you'd rather they hit a curse than a copper, so they don't get +$2.
If you opponent plays a Pirate Ship, you'd rather they hit a curse so they don't get a token.
If you play a Menagerie, you'd rather have a curse than a second copper in hand, so you can get +3 cards.
If you play a Harvest, you'd rather turn up a curse than a second copper, so you can get +$1 more.
If you have Fairgrounds, you'd rather have one curse than another copper, so it's worth 2/5ths of a point more.
If you're being possessed, you'd rather have a curse in hand, so your opponent can't spend as much.
Clearly curse is an excellent card. :-P