I would think that they market the you are attempting to target would dictate what the best platform to start would be. Without knowing your market or idea, this is impossible to say.
Both mobile and desktop apps have their benefits and traffic/search opportunities, but only if targeted correctly.
I am not sure if this helps, but without more info this is the best I can do. I am willing to chat more, if you would like.
I recently came across an excellent post from someone struggling with that same question. I hope it helps you: http://blog.cloudfour.com/responsive-design-for-apps-part-1/
Although I am currently writing a book later out this year, my "day job" is running a creative agency where we've created several responsive websites, including http://newportdunes.com and http://searchoptimizers.com I find that sketching it out first allows for the constraints of the design to focus on what is most important. My favorite tool for this is UI Stencils responsive sketch pad, found here: http://www.uistencils.com/products/responsive-sketch-pad
I know you are specifically asking about an app and not a website, but I think it can still be a useful tool in the "fingers first" thought process and decision process. In Jason's post, he recommends Appcooker.com as a ipad based tool.
I think you'll find that Mobile or fingers first is a fantastic mindset with little downside as it forces you to get clear on the context of your content, size targets appropriately, and then the desktop design does not suffer for it. We sometimes go the other way, too, but we understand what "fluff" we give up when moving to the mobile side. Google Luke Wroblewski for more excellent info on his Mobile First way of thinking.
Good luck and let us know when your prototype is up!
There is a huge difference between the two including capability/functionality, target users, use cases. If you do not know from which one you should start, you probably need to do more homework before getting into development. Let me know if you need some points to assess in order to make the decision.
Some of the other answers here missed your true question of _what_ should be evaluated. I guide my clients around this exact problem. Even though the focus of my business is native apps, I have no problem saying "you don't need an app for that". With more details I could help you further, but in general you're asking:
Who (is using the app) - millennials and retirees use devices differently
Where (is it being used) - is it mostly going to be used on mobile? is it an extension of something else
What (kind of experience) - Web/Desktop/Mobile all have different UI conventions and limitations
That's really just the beginning! As you understand the idea better and the targets, it should become more obvious which is the better choice. If you want to call me, I can provide more detailed suggestions about an appropriate route to take with more information.