I haven't really had security problems to test those features, but as far as privacy, it was pretty clear that they were in fact sharing my browsing history. My Chrome browser and Facebook both started giving me ads that were clearly based on my use of the Brave browser, and I never logged into either Google or Facebook (or any other site for that matter) with it.
There is no way Brave was sending data to Google (Chrome). It was likely the result of using Facebook or some other app that did on both. Brave is very anti Google and it's whole mission is counter to what they do.