One key difference with Bitcoin is that, unlike Bitcoin, Ethereum has an account based architecture. In other words, you have an account that is credited or debited, and you then have a current balance for that account. If you need to get your balance or send ether, you just look up a single number.
Bitcoin on the other hand uses an "Unspent Transaction Output" architecture. Basically your balance is made up of all of the credits and debits (inputs and outputs) you've made with that account. So sending bitcoins requires referencing "unspent outputs".. which may be lots and lots of different transactions.
That's one difference, and there are others, such as the time taken to confirm blocks (current block time on ethereum is 16s). But there are still lots of scalability issues to be addressed, which are actively being worked on.
Vitalik Buterin has a great couple of posts on some of the issues:
https://blog.ethereum.org/2014/09/17/scalability-part-1-buil...
edit: Not sure why this was getting downvoted. Just to clarify, in case it seemed like I wasn't answering the parent. The points above are one of the ways in which "every operation must be verified by every node" is less costly on Ethereum. Obviously if it takes less compute time per transaction, you can scale to larger numbers of transactions per second. Ethereum has already passed Bitcoin in this regard, and has hit at least 8 transactions per seconds at one point, while Bitcoin's ceiling is 7 transactions per second. In addition, prior to launch I believe they managed to push the test network up to 25 transactions per second.
Bitcoin on the other hand uses an "Unspent Transaction Output" architecture. Basically your balance is made up of all of the credits and debits (inputs and outputs) you've made with that account. So sending bitcoins requires referencing "unspent outputs".. which may be lots and lots of different transactions.
That's one difference, and there are others, such as the time taken to confirm blocks (current block time on ethereum is 16s). But there are still lots of scalability issues to be addressed, which are actively being worked on.
Vitalik Buterin has a great couple of posts on some of the issues:
https://blog.ethereum.org/2014/09/17/scalability-part-1-buil...
edit: Not sure why this was getting downvoted. Just to clarify, in case it seemed like I wasn't answering the parent. The points above are one of the ways in which "every operation must be verified by every node" is less costly on Ethereum. Obviously if it takes less compute time per transaction, you can scale to larger numbers of transactions per second. Ethereum has already passed Bitcoin in this regard, and has hit at least 8 transactions per seconds at one point, while Bitcoin's ceiling is 7 transactions per second. In addition, prior to launch I believe they managed to push the test network up to 25 transactions per second.