Private Lessons give you the opportunity for one-on-one with your teacher, which lets you focus on your specific needs. If you need help with the music, or with leading and following, or with untangling your feet, or with maneuvering on the dance floor, or with building confidence, or anything else, private lessons can address each of these in detail. Or, if you just feel that you will learn better by having the teacher focus on you alone rather than a group, then you should consider private lessons.
Group lessons give you the basics in each dance: the timing; a few basic figures or movements; the basic information on leading and following. Some people learn better and have more fun in a group environment...and it's less expensive.