I'm still figuring it out myself but from what I understood the differences were that the Zeus Lightning address has a time limitation if the user is offline for more than 24-hours then the payment is returned to the sender. Where as the Minibits Lightning address doesn't. Also, the Minibits wallet can handle ecash along with sats seamlessly, which might be a plus if the user is into ecash. What I'm not so sure about is what happens if the mint operator's server goes down; the ecash is stored on the user's device and any user can run a mint themselves to connect with their client so I think it's easy enough to recover in the event a mint operator gets taken down. I went through the recovery process for good measure by funding the mint, uninstalling/reinstalling the app, and I am in fact in control of my keys/sats so I don't think it's custodial. I suppose a better test would be to restore in a different app altogether.
Discussion
cashu ecash is a custodial iou for sats on the ln node of the mint but the tokens are bearer assets on the device
it offers superior privacy over any other custodial LN solution
the "ecash" will typically be denominated as sats but can also be in usd
the mint can't rug an individual but could rug the whole mint
if users are on the same mint tokens can be sent out of band by dm, text, email for free
Minibits pays any ln invoice as well
there are certainly ways to zap self custodially but minibits has amazing product fit for nostr
send out your balance to redeem sats into self custodial ln channel on Zeus for example
Ah, thanks, that was my confusion; I thought the ecash was the token being stored on the device. Didn't realize ecash was an IOU held by the mint operator. The way it's presented on the website is: "Ecash is a digital barer token that is stored on a user's device, very similar to physical cash."