Are DAG-based crypto currencies as secure as proof-of-work based blockchains?
You need to prove that the witness Selection process is random and independent. Alice can double-spent if she has control over the witness and the network.
Let assume Alice can double-spent, in bitcoin one can wait for 6 confirmations to rule out most of the double-spent. E.g. Seller only sends out the goods after 6 confirmation. How can you achieve this in DAG? since the account is only updated by its' own transaction. On top of that, the graph DAG is very complex compared to bitcoins' link-listed blockchain.
DOuble-spent transactions may get buried by other transactions.