You can do great mobile experiences on web, but it does require extra time and extra thinking. I don't want to download a new app for every new service I want to try, so I will say that there's still space for really good mobile web apps.
Try and not all web apps should have a mobile web app. But there's are instances where a productivity app will benefit from having a mobile app than just a responsive website. I've worked on a couple of web apps that made mobile-first their paradigm and it sucked. Testing sucked. Dev'ing it sucked. We had to sacrifice a lot on usability and experience which sucked a lot. A mobile app would have made more sense than a responsive site. Then again, I used trulia and having them ask me to download their app was just stupid as the app provided zero value to me (their responsive site was perfectly fine).
