As someone who owns both, I would get a Kelly especially if this is going to be your first H bag. The Toolbox is wonderful and I think it can be a dressy bag, if worn with the right outfit. It's lightweight, holds a great amount and is a real conversation piece. But a Kelly...well, that's just an iconic bag that is a wardrobe staple. I can't count how many times I've carried my raisin Kelly and orange Kelly since getting them.
Also, the Toolbox only comes in Swift leather which limits your options considerably. With the Kelly, you have the option of all types of leathers and colors.
If I can provide any more insight, just ask.