Unlike general purpose chains, app-chains (or application-specific blockchains) are specialized around certain use cases. Specialization generally results in more reliable fees, higher performance, custom-tailored user/developer experience, and higher value capture for the app token.
Appchains are said to be self-sovereign because the governance of the consensus layer and the application layer are tightly coupled. As such, app-chains can recover from implementation bugs on the app-layer by hard forking the underlying chain. Self-sovereignty also protects apps from platform risks.
On the other hand, appchains impose a higher need for social coordination. Deploying new dapps on an app-chain or establishing secure cross-chain bridges between app-chains typically requires involvement from the respective communities. Cross-chain composability is also significantly more complex than composability between smart contracts on a general purpose chain.