Generally speaking, the biggest issues when considering the Army Vs Zombie scenario are the following.
- First off, the military is NEVER going to believe they are facing Zombies at first. They will believe it to be a simple mass rabies incident or something. This means they are going to be going in with tactics that only work on HUMANS. They are almost guaranteed to lose a not insignificant number of people this way.
- Zombies travel in groups, or are almost always depicted as doing such once you've got their attention. This is both good and bad: It bunches up your targets, meaning it's easier to see them, but it also means that if your not quick, you will get overrun unless you retreat... and you can only retreat so far before you have to make a stand at your supply base. Any outbreak needs to be ended before your supply base is overrun or you've essentially lost that battle.
- It's not just head shots, it's brain/brainstem shots. That halves the area you can hit and you need to do it at a distance if you want to not get overrun. Most servicemen are not highly trained marksmen able to hit targets the size of a coconut while it bobs up and down, 200-300feet away. Most of them are merely competent. This means they need to get VERY close to be effective.
- Bullets tend to be deflected by curved surfaces, like heads. This means you need to be dead on if you want to kill something via headshot or you may risk the bullet deflecting enough to keep most of the brain intact, even if the shot hits. As pointed out in WWZ, this can lead to panic and misinformation about what is effective, which KILLS morale.
- Military weapons use full metal jacket ammo for it's penetrating power, ease of manufacture, and because of Geneva Conventions on what is and isn't allowed to be used against humans by military forces. You don't want penetration against Zombies, you want stopping power, which usually means frangible rounds or hollow points, which are used almost exclusively by civilians and civilian agencies BECAUSE they drop a man much faster (and because they won't travel through the wall and hit the innocent neighbors). This is why "heroes" in Zombie movies do more damage with guns off of cops or found in stashes. Unfortunately, the military doesn't have vast supplies of alternative ammo and no time to make them.
- Lastly, you have to deal with Morale. Generally speaking, military forces have higher morale than non-military ones, but this doesn't take into account the fact that your facing
the walking dead, in your home country, maybe even your home town. Your going to have a serious desertion problem, which means less men and likely less equipment, as they will likely taking their kits and vehicles to save their own friends and families.
So really, there are a lot of reasons why the Military is going to lose the first few engagements at least. They WILL eventually get a clue though, which is why any good Zombie Movie ends with the Army showing up to save the day!