Microsoft may have named it "Personal Shopping Assistant", but I'm going to call it "Personal Shopping Snooper", because it most likely spies on everything you do. I don't have any objective information to back that up, but let's face it... Microsoft's credibility has gone straight down the toilet, so nothing they make can be trusted.
If you want to compare prices online, I would strongly recommend doing it the old-fashioned way: by visiting multiple sites, and manually comparing what they have available. I know, that's not new, it's not the most convenient, and it certainly isn't going to get Microsoft any new spying opportunities. But, at the end of the day, it's the best way to keep Microsoft out of the loop (that is, aside from not using Windows or MS Office).