The length gauge and modified case are not related to trimming brass. They work together to help you determine the maximum length you can load your ammo to without jamming the bullet into the rifling.
Haven't used the Hornady trimmer. Looks a lot like the RCBS trimmer I started out with. A couple years ago I upgraded to the Wilson/Sinclair trimmer and stand. I love the Wilson trimmer. It holds cases by the case body rather than the rim. To me, it's faster and more consistant than the RCBS unit, but probably not a "best bang for the buck" tool. Of the products you reference, I would go with the Hornady trimmer over the Lee tools. But that's what I'm familiar with, so I s'pose I'm biased.