So neutrino is just a protocol & client. The data stays on the bitcoin nodes the client connects to except for what is cached, so from the lightning node's perspective, it's the same amount of storage I believe, but you don't need to stand up a bitcoin node on the same machine. It's remote and it just needs a couple of config options to support neutrino clients. I'm not sure about the privacy preserving features that it has, but my guess is that it scans large sections of the node's chain when it needs to check on blocks related to a channel it's checking on. Not sure about long term concerns, but they can be mitigated by only putting what you're willing to lose, since the tech is fairly new.