On-chain there basically isn't much (close to zero) privacy, but off-chain (LN's second layer) will allow you to enjoy more privacy than ever before. In other words, from zero privacy you go to a decent level of privacy, which is a pretty significant jump in my opinion. The more nodes and adequately funded channels, the more anonymity there will be. At some point people will compete with each other by providing liquidity to LN, and that will make sure there is less hub centralization as some naysayers constantly keep hammering on.