Sorry. I had meant to answer this.
They both train different qualities.
The military press is a pure strength exercise. The push press is more about reactive strength.
Of course both train many of the same muscles but the push press is about storing power and exploding up. If someone were just into athletics it may be the more "valuable" of the two but when you are looking to build strength and you haven't done a lot of extensive pressing before I would advice focusing on pure presssing strength at first. Sometimes people use push press to get more reps at the end...basically a "cheating" movement.
Nobody really should begin training with push press. It requires more skill, expecially in the area of core to extremety recruitment. The military or general overhead press should really come first.
With push press you tend to need lower reps with higher sets. The weights used are much heavier. At the beginning intermediate stage it can be a little harder to progress long and may be a little too fatiguing. The other problem is that if your reached a really bad plateau and wanted to switch to MP's you'd have to take a ton of weight off the bar whereas if you switched to push press from MP's you'd get to add a bunch
and push press is a great way to break plateaus. Seated press is another options. Dumbells, whatever.
You will want to train both down the line but for now I'd be doing MP's.