It becomes apparent during the vampires-in-the-military segment that the dude was imagining military service to be like Splinter Cell where you're left alone for long periods of time in dark locations where you can stalk and kill your prey. The only problem is that the vast, vast majority of meeting engagements in modern conflict take place during the day and at ranges of 50-300 meters. Not to mention all of your squadmates whom you're constantly around and who would notice that your mouth is constantly stained with blood and that shit wouldn't fly.
1. Quicker, stronger, naturally better killers
There are tons of jobs in the military, and very very few of them require you to kill with anything approaching regularity. When there is killing to be done, it's at rifle ranges (50-300m), which sort of nullifies the fantasy melee-combat in which a vampire is supposed to excel. As for being quicker and stronger, PT tests are used to measure and document fitness, and I don't think I've ever heard of someone who did supernaturally well on a PT test. You'd think someone who ran a two-mile in four minutes after 160 push-ups and 200 sit-ups would have rated an article in the Army Times or something.
2. Free and easy access to blood
This is not Wolfenstein and you're not at 1 health. Besides, you'd actually have terrible access to blood. See above for my comment re: rifle ranges. Also, when would you be alone with a corpse whose blood is fresh enough to feed on? Do you know how quickly a dead person's blood coagulates? Running to the spot where you just dropped a guy so you can feed is usually crazy dangerous and puts your squadmates in danger. You want a job with a lot of access to blood, become a fucking surgeon. It pays better too.
3. More aware of our surroundings to satisfy our deep-down killer instincts
In Kuwait it got up to 54°C (130°F) and the sun was goddamn unrelenting. It's terrible for even non-vampires under those conditions. Your hunter-of-the-night instincts aren't going to help you when sandstorms have turned the air an opaque orange and you have to cover your entire face to keep the wind from crusting your eyes shut. The military actually teaches situational awareness, and while some people are indeed naturally better at it than others, knowing what is and is not extraneous information while keeping your head on a swivel goes a lot farther than echolocation or whatever superpowers the person you happen to be asking has decided vampires have.
4. Will know where the enemy is before the enemy knows we are there
Again, I don't know what sort of scenarios this person was imagining but hunting for Taliban in mountainous eastern Afghanistan is not the same as swooping down on a big-titted college girl with a broken high heel in a dreary alley, which is something they probably imagined immediately after. In any case, there's an entire sub-discipline in the military devoted to letting fighters know where the enemy is, but hey, I guess drinking blood pretty much renders that unnecessary.
5. We are the best that they have for fighting for our country
6. "Hi Isfahan"
I didn't want to disappoint.