The primary difference between the two are twofold;
a) Scalability. The web scales up better than RPD. Primarily this is because the amount of resources per user goes up faster in RDP then when on the web.
b) "Reach" - by which I mean that pretty much every device has a browser (well every device that could run an RDP client has a browser) and there's nothing for the user to do - they just point their browser at the site and away they go. RDP on the other hand has to be installed on each device, so the user can only used "pre configured" devices to access your servers.
I suppose an ancillary part is that the Web has _limited_ access to the hardware, but it does have some access. A web page can save data locally (although NT6 does not do this) and has access to the GPS. In the future you may see more of the hardware being exposed to HTML (like the camera) but there's no guarantee of this.
RDP though has, as far as I know, no access to the hardware layer at all. It's simply a portal to another machine. Whether there will be developments in this area I don't know.
Some ancillary issues;
Screen-size. Windows apps tend to be designed for fairly large resolutions, and tend to be optimized for mouse input. and they don't really lend themselves terribly well to "no right click" and "big stubby fingers" for input. It's do-able, but you need to allow for that market when building your app. It's a lot easier to do responsive design on a web page because the web is designed for screens of all sizes - and of course really small interfaces for phones become possible.
Development effort and cost is obviously a factor. It takes more work, and more effort, to create a native web app rather than just putting a windows app on a server. If your market is small it can be hard to recoup the cost of that development.
There are pro's and con's to both approaches, so ultimately it's up to you which one you choose.
Cheers
Bruce