[1] https://bitcointalk.org/index.php?topic=195.msg1611#msg1611
[1] https://bitcointalk.org/index.php?topic=195.msg1611#msg1611
There is a lot more bitcoin wrapped onto ethereum that there is on lightning. (Now 1% of total supply). Ethereum is eating bitcoin.
[1] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3160279
[2] https://coingeek.com/bitcoin-script-is-turing-complete-scryp...
These redefinitions say that you can take a few computation steps per Bitcoin block and save their state such that a later block can take a few more steps, so over time, very slowly, spread out over many blocks, Bitcoin can also implement an arbitrary computation. This is theoretically cute but otherwise useless.
Ethereum has a Turing complete language that is only limited in practice by external constraints like the gas limit. Bitcoin doesn't have such a language.
It's partly why Bitcoin is 5x Ethereum's market cap, despite technically being less capable. It's less capable of losing money, of DAO attacks, or other serious failures too.
This can even be proved from first principles: bitcoin, and blockchains generally exist to validate the execution of contracts which have already occurred in meat-space. Basically you and I agree to conditions under which some money is transferred from me to you and vice-versa, which is the actual contract, then write a program (the "smart" contract) which validates that those rules were faithfully executed. It can be shown though that any Turing-complete contract rules can be validated using a non-Turing-complete language like Bitcoin script (ignoring runtime limits). The block chain doesn't need to run every contract, it just needs to validate that every contract ran correctly. A different problem, for which Turing completeness is not required.
Edit: For the down-voters, show me a Turing-complete contract that can't have its execution trace validated in a non-Turing complete language. In the 10 years I've been in this space I've yet to encounter a single one.
SPARK[0] isn't Turing complete but it's still pretty useful, and likely a better language than Solidity.
[0] https://en.wikipedia.org/wiki/SPARK_(programming_language)