Most of my work over the past few years has been either servers exposing their functionality via REST or WebApps that render their own GUI and interact with said servers.
I've avoided the browser incompatibilities issues by exclusively using Chrome. Could have done the same with FireFox - but I somehow like WebKit browsers and the CONSOLE.
I'm still learning and finding the optimal architecture is hard. For example, I programmatically construct the browser based GUIs. It's very much like using WxWidgets or any other GUI toolkit once you get the hang of it.