The Bandit is a single trigger boxlock, the DLX, a double trigger sidelock (with external hammers, as has been noted). If you research the subject thoroughly, you'll find that there are strong opinions on both sides as to which is "best", boxlocks or sidelocks.
I personally lean toward sidelocks (especially the traditional open hammer variety). Boxlocks tend to be a bit cheaper to build, hence the price difference. Note that I said "cheaper to build", not "built cheaply". Both being new Huglus, they should be the same quality, just a different basic design.
I've always had a thing for double triggers and open hammers. Partly, I suppose, because I like the aesthetics, but there are practical reasons, too. I'm a hunter and I like being able to confirm that my hammers are cocked without taking my eye off the game. I've learned from experience that, when a boxlock breaks or a screw comes loose internally, the whole mechanism usually jams. Conversely, double trigger sidelocks are essentially two separate single shots mounted on one platform - if one side malfunctions, the other side still works. Also, side plates can be opened up without removing the stock. I do my own repairs, so this is a nice benefit.
NB: If this post inspires you to remove your side plate(s) for the first time, be cautious that you don't bend the lock plate in the process.