The bottom line is that this is not a simple decision and as most other things, the specifics are what determine which is best for your situation. Don't let anyone tell you which is best without them first understanding all the specifics of your project. Having said that, I will include a few things to think about and include a little of my opinion based on what I have experienced running a software development business that does this type of work.
When you do the development for the MVP you have to answer some questions before deciding on the technology. Is the goal to have a native app, or is the goal to provide certain functionality? If you decide that the latter is the goal, does the app have any functionality that requires it to be a native app? These days, there are very few things you can do in a native app that you can't do with a web app.
Will your app be purely a native phone app or will it also have a web component? If so, this favors starting with a responsive web app.
Will there be a central database or service involved? If it will be connected to a central database or web service, this favors the responsive web app. Otherwise, this item is neutral as far as which way to go.
Will being in the app stores give you a marketing advantage or do you expect most of your clients to find your app through other channels? The advantage here goes to the native app since the app stores don't like websites veiled as apps.
What platforms do you want to support? Android, IOS? What will you do with those that have a Windows phone or some other option? Do you ignore them because they are a small percentage or do you provide a responsive web app? How will your app look on a tablet?
If you want the widest reach, a responsive web app will be needed anyway. If you are only targeting a single phone, then a native app may be the answer. As far as cost, my experience as a developer has been that I will release a responsive web app for less money than a single native phone app. Now multiply the native app cost by the number of platforms you want to reach and you will quickly see why most of my clients start with a responsive web app before going native. Only a small portion of them ever get to the point that they decide to go with a native app after having a responsive web app. By doing this, they saved a fair amount of money.
If your app requires functionality that can only be delivered with a native app, then the question is easily answered...go native. However, in most other cases, I would suggest the responsive web app as your best bet as far as reach and cost. Then if the application is making money, you can afford to build the native app.
If you would like to discuss this with more specifics, feel free to reach out to me on FD or LI.
Good luck on your endeavor.