Each of these works in a different way to control acne.
Benzoyl Peroxide is for most people the first rung on the ladder of acne treatments.
It's easy to use and is safe to use in pregnancy and can be used in combination with other treatments. For the majority of mild acne sufferers Benzoyl Peroxide is an effective treatment that is relatively inexpensive. It also comes in a variety of strengths and formualtions (lotions, creams, gels) that suit various skin types.
Benzoyl Peroxide does have some downsides.
It can be irritant when you start using it. This isn't usually a big problem, and can be minimised by a gradual increase in use. Because of the way it works, breaking down skin oil (sebum) and dead skin cells (keratin) it can lead to a drying of the skin. If this is a problem Dr Amanda Oakley suggests using a light moisturiser.
As it's name suggests (Peroxide) it can bleach colours from clothing and bed sheets. Be careful, make sure the cream or lotion is completely dry before your skin touches clothes or other material that might bleach.
Vitamin B5 or Pantothenic Acid is usually absorbed from food we eat Mushrooms, whole grain cereals, wheat bran, alfalfa, and rice are geat sources of B5. The problem is that the dose required for an treating acne is much higher than what we can easily get from our diet.
There's arguement over how B5 works to improve acne, one school of thought is that an excess of B5 changes how the body deals with some fatty acids. Unlike alot claims that are made for vitamins and health treatments there is data behind using B5 for acne.
Azelaic Acid is a natural product. It's found on normal skin where it's produced by a fungus that naturally lives there called Malassezia furfur. Azelaic Acid works by killing acne causing bacteria in skin pores, and by decreasing keratin production. Acne causing bacteria use keratin as food.
Azelaic Acid doesn't appear to increase bacterial resistance to antibiotics, and doesn't stain or bleach clothing. Unlike retinoids (Adapaline) it doesn't cause sun sensitivity.
Azelaic Acid can cause skin irritation in some people with sensitive skin, or with a history of eczema.
Adapalene is from a family of medicines called retinoids. Retinoids are chemically related to Vitamin A, and so need to be used with caution in pregnancy.
As well as being effective for acne, retinoids like adapalene are sometimes used for treating sun damage (photoaging) and reduce fine lines.
The downside to topical retinoids is that they can make the skin very sensitive to UV while treatment is on going. So it's important to use them carefully, and use a good quality broad spectrum sunscreen. They can also be irritant, and can take a bit of time to get used to.