My rule of thumb (which pretty much merges with @DA01's comment), is "Do as much as you can, but don't do more than needed".
Maybe, if you wanted to give each platform its different design guidelines to appeal everybody, you could simply make a native app (do as much as you can). They tend to be a better choice for users, rather than accessing a website, and if you wanted to put your web app into an app using phonegap, cordova or whatever technology, they tend to be much much less touch responsive than a native. Terrible drawbacks, is that you'd need to design and develop both apps (don't do more than needed). The codebase could be the same, into different languages, but anyway you'd still need to make a looooot more work.
On the other side, I think we all get used to platform-agnostic web designs on mobile devices. What I'd never recommend is to stick to a platform when thinking on designing a mobile website. Haven't you felt cold sweat when navigating though a mobile site with the top back pattern from iOS, using a design style from iOS 3 or 4? If you use a simple, responsive design, you're good to go.