I'm firmly in the mandoline camp. The break even point comes at about 200 g of vegetables for me, below that knife is quicker because of the cleanup time. It also doesn't add to your electricity bill and is by extension environmentally friendlier than running a 0.5 KW food processor daily. If your knife speed is different, your break even point will be at another amount.
Because a real food processor requires much more cleaning, I find that the break even point for it vs mandoline comes at about 800 g of vegetables.
I have never made good experience with small handheld choppers like the one in your first link. Maybe I just happened upon bad products, but they were clumsy and didn't cut well. A good use for them is raw onions - the enclosed cutter reduces tears because only very little of the vapors escape.
I have never used tools like your second and third link. But I'm very skeptical about them. If their cutting surfaces aren't razor-sharp, they will smash the vegetable rather than cut it properly. You'd need a softish vegetable for them anyway, I doubt that they can do carrots or potatoes. Even if they are perfectly sharp when you buy them, they will go dull with time and there is no way to sharpen them.