Bitcoin doesn't try to prevent copying (which is
physically impossible), it tries to prevent
double-spending, which is a completely different beast. There is no need to prevent copying since there is nothing to copy: bitcoins are not actual pieces of data and do not even exist in their own right, instead what you have is a list of
transactions. Since all Bitcoin transactions are public, any transaction which spends coins which are already spent will be detected and rejected by the network. Mining prevents transactions from being fraudulently removed or altered by hashing each block of transactions (and making that hash difficult to calculate, but easy to verify), and making each block dependant on the previous block's hash, which makes it (practically) impossible to alter a block without invalidating all the blocks that came after it, causing the altered block to be rejected by the network.
DRM, on the other hand, is
fundamentally flawed:
In DRM, the attacker is *also the recipient*. It's not Alice and
Bob and Carol, it's just Alice and Bob. Alice sells Bob a DVD.
She sells Bob a DVD player. The DVD has a movie on it -- say,
Pirates of the Caribbean -- and it's enciphered with an algorithm
called CSS -- Content Scrambling System. The DVD player has a CSS
un-scrambler.
Now, let's take stock of what's a secret here: the cipher is
well-known. The ciphertext is most assuredly in enemy hands, arrr.
So what? As long as the key is secret from the attacker, we're
golden.
But there's the rub. Alice wants Bob to buy Pirates of the
Caribbean from her. Bob will only buy Pirates of the Caribbean if
he can descramble the CSS-encrypted VOB -- video object -- on his
DVD player. Otherwise, the disc is only useful to Bob as a
drinks-coaster. So Alice has to provide Bob -- the attacker --
with the key, the cipher and the ciphertext.
Hilarity ensues.