I haven't seen or used those touch up kits, but knowing paint, how you apply it and over what will make a huge difference. I'm sure the touch up kit uses the exact same pigments that they put on at the factory except formulated differently for the layman to just brush it on.
The darkness is mostly coming from dabbing or brushing on the paint, which puts down a ton more pigment than spraying it. The cardinal red may have also been applied as a three stage paint job at the factory - metallic/silver layer, transparent/candy red layer, then clear coat. That process will produce quite a different look than brushing on the paint or even just spraying the metallic red as a single layer.
It's a lot of work to spray a seemless looking repair. I would feather sand the damage into the surrounding paint, feather spray the primer, feather sand that to blend, feather spray the touch-up paint to blend with existing paint but DO NOT sand that as sanding metallic paints will ruin it. If you have to sand to blend the paint better you'd best use high grit sandpaper (1000 grit) to try preventing damage. Finally feather spray the clear coat and wet sand to blend in.
You can see why most paint shops would rather strip all the paint and start fresh and why a good repair job will cost you some money. Not worth it to repair small chips and such.
