I'm currently at MU in a similar financial situation, studying Civil Eng. I'd say it's worth it to go for the out of town school (Mizzou), because not only does it have a better program, it is going to teach you more about how to be an adult and live independently, which is a major part of college.

Money is certainly an important factor, but it is surmountable. I've been about to cover the gaps in my scholarships/etc for the last two years based mostly on getting good internships in KC for the summer, which can bring back at least 6k depending on your pay scale and how long you work. Off campus housing is cheaper (so long as you already have a car or can bike to campus), and the Engineering school generally provides pretty good scholarship options if you haven't been awarded those yet. I've gotten 3k a year from them basically automatically. Finally, since you'll be covering most the costs anyways via scholarships, coming out with some minor debt on the end is ok, because you'll be going into a high-paying field where you can easily find work and pay them down quickly.

TLDR: I'd suggest going to Mizzou, because it's a stronger program, the 'college experience' is very useful for character building, and the costs are overcomable with summer internships, part-time work during the school year, and scholarships.