Europeans seem not to tip guides for paid tours. Americans sometimes do. I've only taken low-priced walking tours, so I have no idea what goes on with pricier tours.
As for the "free" tours, Rick reported several years ago that the free-tour guides had to pay their company about 3 or 3.50 euros (I don't remember which) for every person who took the tour, however much they did or did not tip. What a racket! I try to avoid those tours, but sometimes they seem to be the only game in town. In that case I usually tip about what I'd expect to pay for a paid tour.
People seem to love the idea of a "free" tour, so the free-tour groups are likely to be larger than those on paid tours. In addition, I think you are a lot more likely to get a licensed guide on a paid tour. I just don't have total confidence in the accuracy of the information provided by unlicensed guides. On a "free" tour, the guide makes his living by entertaining one-time customers. It must be tempting to make things as exciting as the imagination allows. That said, I had no problem with the guides on the free tours I took.