The worst ones are those that imply you can save money by using Sheepline, which of course is under no circumstances actually possible compared with booking direct with the relevant TOC.
If the relevant TOC doesn't use TrainLine as their backend, then it has occured in the past that tickets have been cheaper via The TrainLine than the TOC's system. This is mainly a function of the routeing and itinerary algorithm behind The TrainLine recognising that changing at different stations, which some booking engines may consider 'equivalent', might actually impact the price or availability of through Advances.
For example, for some journeys there are multiple stations at which the trains you want to change between call at - e.g. if travelling Liverpool-Bristol using a WMT Liverpool-Birmingham service and a XC Manchester-Bristol service, you can change at any of Stafford, Wolverhampton or Birmingham and end up on the same trains, just starting/finishing at different points.
Some booking engines consider itineraries changing at each of these stations exactly the same, as the journey time and number of changes will usually be the same, and so they will by default have you change at the station marked as the largest in the data.
However, The TrainLine, as well as other smart booking systems, will try each change point to see if this enables Advances to become available at all where previously only walk-ups are available, or if it enables cheaper Advances to become available. Sometimes there is a difference, depending on the 'tier' of Advance permitted on the train in question.
However, if the TOC uses The TrainLine then the price of the tickets themselves will of course be the same on either website - it will only be the cost of ticket pickup and/or booking fees that varies. And in any case, this kind of scenario is very rare indeed and the price difference is not usually significant.