I’ve been using it for about two weeks now, and as a British English speaker, I feel it can capture my accent when writing the vast majority of the time. My minor complaints about it so far are the places where I feel it isn’t unambiguously capturing my accent (the other commenter mentions 'R’s, that’s one of the issues).
Perhaps another important metric to measure it by would be whether people can reliably hear my accent when I write too.

I looked a bit into Quikscript, but I think that with the traction that Shavian has (unicode support is a big deal), and the fact that I’m not particularly interested in writing by hand, I thought Shavian would be a good start.