Welcome to the forum. I too have been cross-shopping these two cars and am leaning towards the Mitsubishi. You are, of course, asking an unknowable question - one that we would all like to know. Here are a few thoughts:
The Honda Fit, 1st and 2nd generation have been reliable. The 3rd generation likely will too, but there is no way of knowing that - completely new car, made in new facility. The Mitsubishi is new to our market, but has been in production longer. The Mitsubishi also doesn't use direct injection, or other advanced technology to achieve its goal - it uses basic physics, being more streamlined, lighter, and lower displacement (there really is no replacement for displacement after all).
You plan on putting on the miles quickly. That suggests that you will save a bundle with the Mitsubishi's fuel consumption numbers. Lets assume the Mitsubishi needs a bit more repair in years 8-10. Would those repairs really cost more than the anticipated repairs for the Honda + the $1000s in fuel savings. Especially when you consider that everything on the Mitsubishi is a bit smaller and less complex (Honda fuel pump will likely cost a lot more). I doubt it. I am driving a 2003 Ford and doing none of my own repair work, and still my repair costs are under $1000/year currently (alternator, CV boots, brakes, that sort of thing).
We seem to be living in a golden age of engine/transmission reliability. I just don't hear of engine/transmission failures much any more. Mitsubishi's 10 year warranty might not apply to you, but highway driving/steady state isn't very hard on a vehicle, so I doubt you would have any issues assuming you change the oil on occasion.
The Honda is not more expensive because of reliability. It is bigger, more powerful, and more luxurious. I think of the Mitsubishi as what Honda was in the 70's, a small, efficient car without a bunch of bells and whistles.
Here are a couple other threads you might be interested in (forum has a search function, top right).
http://mirageforum.com/forum/showthr...ht=reliability
http://mirageforum.com/forum/showthr...ht=reliability
http://mirageforum.com/forum/showthr...=cross+shopped