The main advantage for native applications is that they can access all native APIs a platform could offer (contacts, camera flash, SMS, telephony, network, bluetooth, sensors, raw sockets...) while a progressive web application can not (yet) as they are constrained by the Standard Web capabilities.
The goal for progressive web applications is to expand these capabilities to cover the most critical cases. In this mood, take a look at Progressive Web Apps: Escaping Tabs Without Loosing Our Soul where you can find a list of what a progressive web application should offer:
- Responsive: to fit any form factor
- Connectivity independent: Progressively-enhanced with Service Workers to let them work offline
- App-like-interactions: Adopt a Shell + Content application model to create appy navigations & interactions
- Fresh: Transparently always up-to-date thanks to the Service Worker update process
- Safe: Served via TLS (a Service Worker requirement) to prevent snooping
- Discoverable: Are identifiable as “applications” thanks to W3C Manifests and Service Worker registration scope allowing search engines to find them
- Re-engageable: Can access the re-engagement UIs of the OS; e.g. Push Notifications
- Installable: to the home screen through browser-provided prompts, allowing users to “keep” apps they find most useful without the hassle of an app store
- Linkable: meaning they’re zero-friction, zero-install, and easy to share. The social power of URLs matters.
From these points, linkable was one of the first characteristics imported by native applications from the Open Web in the form of mobile deep linking.
But special mention deserve the combo fresh + installable as it represents one of the main advantages of the Web as a platform over the native alternatives. Here installable means that it appears in your home screen. It does not mean you require to pass downloading and installation stages. You open a URL or discover a service while browsing and it's done: it appears in your home screen.
Fresh refers to how a regular web works, offering an instant load and seamless updates. You are not asked for installing an update from the web of YouTube, it is deployed and you consumes it the next time you visit it.
I'm not talking about the benefits of the remaining points because you were asking for the differences and, for instance, re-engagement is something native applications already have via push services and notifications and now web applications have caught up.
Other related and key question is about which platform is more suitable for your needs. If you are not accessing special hardware capabilities, the Web should be enough and choosing the web you are free from the marketplaces, proprietary ecosystems and by the way, you can ensure certain grade of ubiquity and interoperability.
As final notes, I recommend you to browse www.flipkart.com from a mobile with Chrome. It's pretty awesome: no bugs, smooth navigation, app-like feeling. Go offline and it will continue working. A truly real world example of that post. Add the app to home screen and next time you open it, the experience is even better.
You can take a look at Firefox OS as well as an example of bringing more platform APIs to the Standard Web (with more or less success).