Both of these frameworks have too much baggage for me. My bundle size tends to be rather large with each option, though both support tree-shaking. I prefer Vuetify for content sites and ecommerce and Quasar for building actual applications, because the components are very intuitive and much easier to use together in odd combinations than Vuetify: everything "just works" together with very simple and consistent styling and APIs.
If it were me, I would use Gridsome or Nuxt with Tailwind and minimal dependencies. You get a great DX still with tailiwind, good "tree-shaking" through PurgeCSS and nothing you don't need, with full control over your own components.
Quasar and Vuetify are two entirely different beasts - so your decision depends on what you need:
Quasar is a framework to develop multi-platform apps from the same code base. It supports mobile apps, websites (SPA or PWA if you want) and desktop apps. It comes with a build system and also with a UI framework (visible components).
Vuetify is a UI components library. So if you only need that, it might be the choice for you.