I have a Lily - a lovely instrument, I have no experience of the other model, so couldn't comment, as stated the Lily is a single voice and can be a little different to listen to. Mt Father in Law plays his Lily a lot, he says it is an old man's instrument on the theory that with it being small, it is easier to lift and play than his Paulo Soprani!
The lily is very responsive, and sweet sounding, easy to carry and a great little box, perhaps someone with knowledge of the other may have their opinion!
Cheers, Lucy