It seems to me that once Casper is fully implemented, the best of both worlds would be for the valuable and scarce BTC token to live on the expedient, efficient Ethereum blockchain. But would this be technically feasible?
Quoted from Vitalik Buterin on Reddit: (https://www.reddit.com/r/ethereum/comments/4d5z1y/is_it_possible_for_bitcoin_to_live_on_the/)
"BTC -> ethereum convertibility can be done fine; the hard part is the ethereum -> BTC conversion. There would need to be some kind of sidechain protocol that can "understand" receipts being created on the ethereum blockchain; this is nontrivial and would have to be done as a softfork and accepted by BTC miners; if you don't want to do this, then the two alternative routes are (1) a federated multisig peg with independent and known parties, and (2) a multisig peg with security deposits on ethereum to incentivize participants to sign transactions correctly. (2) does rely on ETH continuing to have value and not dropping too quickly though, as otherwise the collateral may suddenly be insufficient to provide an adequate incentive not to steal the BTC.
I'm not an expert. But you can implement any currency in Ethereum. So nothing prevents you to do so.
However, everyone (at least every miner) would have to agree at some point and make a migration process. Something which freezes bitcoin network transactions forever, and the only possible transaction is paying TO "someone" who grants the owner of the sender account bitcoins the same amount of "Ether-currency". This kind of change (changing the rules after all) probably needs something like a hard-fork @ bitcoin network too.
And of course, everyone has to trust that "someone" (or at least the mechanism which makes it safe). As he would basically be destroying bitcoins and creating ethereum.
Another interesting discussion would be performance and robustness of both networks (which I do not fully understand).