"Is southern food sweeter than northern food?"
Actually, you can omit 的 for 南方的农业 or 北方的生活, but it would not "sound" as rhythmic. We Chinese like to pair a 2-character adjective with a 2-character word because it sounds nice. In this case, a 的 can separate the two pairs of characters and make it sound nice.
For your information, 南方 alone can be a noun, but it can also be an adjective, e.g. 南方人 = the people living in the South