I might be wrong here, but the two major problems with browser crypto were the fact that you had to send the crypto libraries to the browser in the first place,

I might be wrong here, but the two major problems with browser crypto were the fact that you had to send the crypto libraries to the browser in the first place, and that then you didn't really have access to a proper random number generator. Those two issues pretty much disappear with the use of a built in api from the browser. I guess now you've just got to trust the browser, but the browser is never going to be as secure as doing things on your own server.