as someone who has studied both, I would recommend LUSD (v1) over dai. LUSD was launched 3 years ago, so it stood the bear test. the minimum collateralization ratio of 110% applies to individual troves as long as the total system collateralization is over 150%. once that's breached, troves are required to have 150% minimum. the Achilles heel is the oracle. if Chainlink pulls the rug, which they can, it's over (sadly, Tellor is used by Liquity in a way that it can't protect against a Chainlink apocalypse). Maker is somewhat better in this because they use Chronicle, which is ran by more trustworthy people, but I'm almost sure they haven't made their contracts immutable. if that is the case, then the same attack vector exists there.
as you'll see, neither of these are the solution we're looking for, and they both run on the no-privacy, hypercomplex, captured, constantly changing Ethereum blockchain, so... fuck.
but dai for a long time has not been what the market thinks it is. avoid it.