Before I start listing why a mobile website is better I just want to mention that this is simply a light comparison and that your decision should depend on the features and functionalities your business or concept needs. I will give you two scenarios.
You provide a social networking service or perhaps communication where users use the service for extended time and need to interact with their mobile device components such us cameras and locations. Moreover you can offer push notifications to engage your clients directly. This looks like it calls for a mobile app rather than a mobile website. However, you have a pizzeria business where people chose ingredient and order pizza and you deliver it for them I would advise you to consider a mobile website considering the following points
Mobile websites can reach larger Audience faster
Mobile websites are published on the internet just like any website. Anyone using search engines to find products and service can find then given they are optimized and marketed properly. The chances of a potential customer downloading your app just for a quick solution is slim compared to simply going to your mobile website and get done with it. Moreover once your mobile website is published basically everyone gets one. you don't have to cater for the iOS and the android. Last but not least it is easier to share a link rather than an app.
Mobile websites are built faster and cheaper
The worst thing to own is an under budgeted mobile app while you can own a splendid mobile website that can help your business equally if not better than a mobile app. Apart from the rigorous development cycle that mobile apps need to go through you will need to build at least two mobile apps one for android and one for iOS to cover all your potential clients this shoots the development cost way higher than the cost of mobile websites.
Mobile websites are updated and upgraded instantly and as frequently as you want
This is my favorite point, one minute your client is looking at a page and next minute poof ! Brand new mobile app website no uninstall and reinstall required. Especially if you have a business that needs regular updates of user interface or adding features and functions frequently getting your user base to update the mobile app and not decide to no longer keep your mobile app in their phone may be a tricky business.
Mobile websites are cheaper to maintain
Last but not least deploying a mobile app is not as easy as just publishing it on google play and istore. You will need to monitor, evaluate and optimize. Updating your mobile app requires planning and the whole cycle of monitoring, evaluating and perhaps optimizing too all over again. troubleshooting usually takes more than just a browser, sometimes you actually have to have a physical device. Tis makes the maintenance and services more expensive that maintaining a mobile website.