There is always going to be a debate over these two ingredients. Natural versus synthetic. You'd think natural would always win, but in this case, there are arguments to be made for both sides.
Fragrance Oils are synthetic, man made with essentially inert ingredients. Unless you happen to have an allergy or a sensitivity to one of the components they are very safe to use. In fact, they are often safer to use because so few people have any kind of a reaction to them. Also, they provide such a broad range of amazing scents, virtually anything your heart desires.
Essential Oils are natural, usually pressed or steam distilled from the natural plant material. They have wonderful medicinal properties. For example, Rosemary Essential Oil is wonderfully invigorating. It can help with exhaustion, muscle cramping, arthritis. It can revitalize dry and dull skin, help keep dandruff under control and encourage healthy hair growth. Sounds great, right?
However, you know how the medicine commercials are now filled more with warnings than the benefits? Essential Oils need to be treated the same way. Rosemary Essential Oil should be avoided by those with high blood pressure. It also should be avoided during pregnancy and those who suffer from epilepsy. It can cause severe complication for people with these conditions.
I've spent years researching essential oils and their uses. I also am very blessed to have a certified aromatherapist in the family (my mother in law). I've developed a very healthy respect for essential oils, all of their properties (good and bad), and use them carefully.
So which should you choose? That's completely up to you. I personally use both in my products. I love being able to use natural essential oils, and I also love to use unique and exotic scents that are only available to me in a fragrance oil. My only caution is this. If you choose essential oils, make sure that you trust the person creating your bath & body products. Ask them questions about their knowledge in the aromatherapy field. If they know their stuff, they'll be more than willing to share that with you.