My 2 cents, I have been a toolmaker for 16 years now, everything from grinding/fitting to trodes, to cnc programming/milling which is where the majority of my experience lies. I would say go with the tool and die, I assume it's more involved and more precision based teaching/thought processing. Any shop you go to will teach you what and how they want things done, and I haven't seen a good tool shop that doesn't have good programmers and cnc guys. I was given a choice to get more in-depth with either burning or cnc milling, I chose milling/programming since it's more "transferable" so to speak if I ever looked for another job. Get good running a mill and programming for a tool shop, you can get a job anywhere in a job/production setting, although you would probably find it boring after being in a toolroom setting for any length of time. Good luck!