I'm on a Lumia 1020 with Cyan, 8.1 and update to 8.1.
I'm experiencing instant crashes as soon as I search or click on a link in the menu such as Google Search, and also many crashes as soon as opening the app.
It was working better in the initial release, even though searching often crashed and sometimes the browser didn't load anything (parsing error).
Happy to help any way I can!