Either one will work. I suppose it depends more on the terrain you'll be hunting in. If loooong shots are possible, take the 7. If regular ranges (up to 200 yards) are expected, the .270 will do just fine. If they're close and you can accurately place your shots, hit 'em right behind the ear and they'll drop right there. Otherwise, right behind the shoulder for the lungs will put them down in short order. The heart is a bit lower than deer type animals, so I generally just go for the lungs. I like a bullet to exit on hogs because their fat generally seals up the entrance wound, making tracking a chore. On smaller hogs, when the brush is thick and tracking is hard, I try to break the shoulders to put them down. Beware larger hogs though, they have a pretty stout gristle "shield" over the shoulders that can limit penetration. With good bullets like you're shooting, I'd just hold a bit behind the shoulder about a third of the way up from the bottom and let 'er rip! (exception being the behind-the-ear shot mentioned earlier)
Have a good time. Pig hunting is a lot of fun.