I would actually say a bigger difference is that Bitcoin state is limited to a set of unspent transaction outputs with value (UTXO set), whereas Ethereum allows the script to store arbitrary state in its output.
On a side note, Proof of Stake is a really cool feature if it works, but Ethereum doesn't have it, only the promise that it would hardfork to it if a viable solution is found.
[1] https://en.bitcoin.it/wiki/Script
[2] https://bitcoincore.org/en/2016/02/26/zero-knowledge-conting...
(and yeah, I had to use Fx reader mode to parse the jumble of text at all)