Mobile Apps Pros:-
1. High performance, fast, ability to work offline, keeps handy on device.
2. Can best utilize device resources (GPS, camera, accelarometer).
3. Gets best support from OS and OEM, not dependent upon browser.
4. Running in background, a boon.
5. Handy notifications.
1. Comparatively higher in cost.
2. Multiple code bases are needed to be managed.
3. NO SEO advantage unless you make a landing page for the same and do a good ASO.
Mobile Web app Pros:-
1. Cost effective to start with.
2. Enjoys all SEO advantages that a website has.
3. Good for Investor Demo, early traction purposes.
1. Dependency on internet, always.
2. Low performance, low grade UI and Ux, non priority support from OeM.
3. No app store visibility advantages.
4. Overall customer inclination is towards downloading store apps more than coming to the browser.
5. Mobile apps are more secure (debatable, but its mostly true IMHO).
Source of my knowledge:- I run this mobile app company Agicent Technologies, and we develop all kind of apps and games for startups and entrepreneurs.