I use lozenge on my mares... With that being said I looked at Dr Bristol and french link closely several years ago (to compare), and there is a difference there. Dr Bristol turns vertically putting more pressure. I never tried it on my mares though..
French-link. Note the angle of the rings that connect into the "link", and the shape of the link itself.
Dr Bristol. Once again notice the angle of the link and the rings that connect to it. Also note the straight sides of the link. Used this way, with the flat part against the tongue, it is relatively mild.
However, if turned upside down, the straight edge sits against the tongue, making this bit more severe as the surface area is much smaller. Both are double-linked snaffles and work on a combination of tongue and bar pressure. Single-linked snaffles use bar pressure (and palate pressure sometimes due to the nutcracker action).