Nothing major but annoying to have to deal with everything being broken because of maintenance or whatever else.

AdGuardHome (and pi-hole) work almost entirely on domain blocklists they regularly download from configurable sources (AdGuardHome also incorporates Google safe browsing). This blocks a lot of stuff, but NextDNS also has options like blocking typo squatting, newly registered domains, domains that are created by domain generation algorithms, and whatever their "AI-driven threat detection" feature is doing. It's hard to tell how useful those features are and there's no reason blocklists couldn't incorporate all those kinds of things. But I have no idea if they do, and outsourcing putting all that together to a service like NextDNS seems like a better solution than a locally hosted option that relies on a user figuring out the right blocklists to use. Although NextDNS also allows you to play with blocklists if you want.