Desktop:
pros -> more productive, simpler, stabler APIs and frameworks, easier for « backend devs », more information density, better screen management (multi windows), more access to native devices and features, ...
cons -> deployment / upgrade workflows, dependant on client configuration, usually less portable, easy to leak domain logic in frontend, harder to scale, ...
Web:
pros -> portable, “lightweight” client dependencies (browser), mobile / tablets, good separation of backend and front-end logic, ...
cons -> less productive (generally), require more infrastructure and Ops, harder to fit LOB-apps workflows and information density requirements, many choices to choose from, fast changing, ...
But this is becoming a relatively false dichotomie with web-based desktop apps (electron based or specialized like OpenFin in the banking world).