Mobile Apps and Mobile Websties are different products and available to meet different needs and scenarios.
Mobile Apps are great if you want to serve frequent customers. Native mobile apps are fast and handy for customers who know what you do and what they want from you. Examples include bank making apps to facilitate their account holders.
Mobile apps are bad if your target is new customers. User journey for a mobile app is several times hard to start than opening a mobile website. Mobile Apps are also designed with limited use-cases in view and thus can only satisfy customers who's needs are well defined and understood.
Mobile websites are great to engage new customers and expand on market share. These sites are able to handle wider array of user stories but at the same time require more browsing/searching before a customer is able to reach desired product/service.
Mobile websites are also acceptable for returning customers as they know their path to the product/service of their interest.
Now why is there a need of having a mobile app if mobile websites are doing great? There are few considerations
- Mobile apps can use mobile's native technologies (camera, GPS, local storage, accelerometer and mobile gestures) and are able to offer more engaging experiences then mobile websites can do.
- When a customer installs an app, he/she tends to be more loyal to the organization and would try to use the service through the installed app, reducing possibility of interaction with competitors.
- Mobile Apps offer deeper insights into application usage and user-behaviour.
- Native apps are fast and require less communication with the web-servers, and thus are cheaper to use than mobile websites.
- Native apps are fast to load and use vs Mobile Websites.
At the end of the day it is the organizatioanl need which helps us pick one platform other the other, but both options are available and both are helpful in their respective scenarios.
Jacob Neilson has addressed the same issue and compared Mobile Websites, Native Apps and Hybrid apps on its article Mobile: Native Apps, Web Apps, and Hybrid Apps.
Another discussion on the subject in the context of tablet is available over ux.stackexchange.com