There are a few ways of composting and each has their benefits and disadvantages. Firstly one need to understand how compost is made, and the process is entirely reliant on microbes, there are aerobic(need air) and anaerobic(no air required) the microbes break down the organic material using the nutrients as energy during the process. Some of the microbes break the bonds holding the material together which creates heat, this heat reduces the nutrient values of the compost. The heat drives out the air from the heap and also dries out the heap but at the same time it kills some pathogens and weed seeds, so long as a temperature of above 70 degrees is maintained for several day; this can only be done if there is air during the process because just like a fire when the air runs out the fire cools down. Then the anaerobic organisms get busy some are good and some are not; if you included the effective microorganisms when you built the heap then the good guys will take over and continue the process without air. If not then there is a chance that the bad guys will convert the nutrients into something useless to plants.

Types of composting 
Green Genie compost container

This unit is available from many large hardware stores and it will have a lid and a few holes down the side this is good for very small gardens and generally if its open to the soil, terrestrial earthworms can come in through the bottom and do some work for you. The container process can take up to 6 - 9 months, and these microbes work mostly anaerobically

Turning composter
This unit is more difficult to find and comes in various designs, the idea here is to help you to aerate the compost which will speed up the composting process. very easy to use but comes at a price and not really designed for large volumes. this process can take up to 6 weeks. This compost is best left on the surface of beds as mulch.

This type of unit is the one you would find against a wall, or can even be free standing, and you will recognise it by the siding boards the keep its shape, this works similar to the drum unit in the way in which it makes compost and usually are a minimum of 1 cubic meter in size. this process can take 6 - 9 months these work anaerobically

Free standing static heap
This is probably the most common one that most people have in their garden, it's just a pile in the garden where everything gets dumped, then one harvests the compost about a year later by unpacking the pile to get to the stuff at the bottom. these work mainly anaerobically.
This type of heap can be done in a swale and can be relatively nutritious when built correctly with all the right ingredients and layers. 

Freestanding active heap
These are the most practical and give you similar results to the turning composter which uses the aerobic organisms to break down the material in a short period of 6 - 12 weeks this type of system can be very effective and nutritious if built correctly with all the right ingredients and additives added for health microbes and well bound, plant available nutrients. Main advantages are rats and mice don't move in and you can control the heat preventing nutrient loss from overheating. This compost is best left on the surface of beds as mulch.

These are a very long version of the free standing active heap and are turned by machine the process is usually done in record breaking time and is sold to you while still being digested, so it's normally hot when it arrives and cools while it stands on your property. This compost is best left on the surface of beds as mulch.

Properly made home compost is more nutritious than any shop bought compost because it generally contains a wider variety of ingredients. If it is made correctly it is not allowed to get to extreme temperatures, and it has additives added to fuel the microbes and to bind the nutrients. All, these systems will work better when effective microorganisms are added during the build up of the heap.