I'm the CTO at Brass Monkey. We definitely experimented with this approach of using a webpage and websockets to communicate, it is nice that it doesn't require installing an app but it communicates via relaying messages out to the internet and back and so generally has latency in the 100ms+ (<10FPS) range and usually worse. See early video I made at a previous Company using HTML5 for controllers: http://www.youtube.com/watch?v=NE8-TntjYB4
With Brass Monkey we decided to instead make a single master controller app that used a trick we discovered to communicate over LAN between your phone and PC, this way it's blazingly fast. Can be more like 10-20ms (100-50FPS) instead and more consistent.
You only have to install it only once and then you can play any Brass Monkey experience seamlessly, including auto-pairing tech that detects other instances of Brass Monkey enabled web pages on your network.
Note: There are still major advantages to the web based approach such as bypassing Apple's approval process. It's hard to have controller side code executed unless you bake into your app as Apple doesn't allow dynamically loading code into native apps. But we decided to go responsiveness for our initial focus and are trying to figure out how to bring in some of the other benefits the web page as controller approach takes.
Wow! Could you please tell a little more about the trick? How does a LAN connection between your web app in the browser and your iPhone app work? Do you create a locally accessible web server from your iPhone app?