I've read lots of articles on SoftNote wallet. Here's what I learnt:

• It allows to pay with Bitcoin by using Tectum blockchain. 
• There is no transaction like with usual blockchain wallets, because you do not transfer coins, you transfer the ownership.
• To do that, you use a SoftNote bill, which is like a mini-wallet that you transfer to the person you pay.
• To change its ownership, you communicate a QR code, which is the private key, and a secret code, which adds an extra layer of security.

The advantages are:

• It is fast and simple.
• There is no transaction, and hence no transaction fees.
• It respects privacy, since you do not need to use a blockchain wallet.

The drawbacks are:

• As far as I know, there are not so many merchants accepting SoftNote bills.
• Tectum blockchain does not seem as decentralized as claimed. More information is needed.
• The level of security used for the wallet and the payments is not adapted to huge amounts.

In summary, the SoftNote wallet is an interesting alternative to Lightning network, but more work is needed for the adoption.