The true answer to this question is that the weight and contents of trash have much more to do with its longevity in a landfill than its volume. Compacted Styrofoam still lasts for as many centuries as it does when not compacted. Crushed glass is more of a danger to you handling your garbage bags, and it still takes up space. In fact, organic matter has a tendency to break down even more slowly when compacted, rather than when exposed to the air.
There is also the energy use of the compactor to consider, as well as the environmental impact of their production. Energy used in these processes, as well as the collection and fashioning of materials used, all have an environmental impact, often causing a carbon foot print that you might be better off not creating.
Far better green solutions include composting food matter and organic waste. Use compostable or recyclable bags in a regular garbage bin if you want to be as green as possible. Recycle all materials that can be. Reuse bags, bottles, and jars rather than throw them away. Always remember, the best trash is the trash you don't make. When you consider Reduce, Reuse, and Recycle, it should always be in that order.
If you are charged for your trash collection by volume, you might save a little money on collection fees, so there might be monetary savings with a compactor. However, one should take into consideration the cost of the machine, installation costs, and energy costs before realizing any sort of savings from an industrial trash compactor.
There are other considerations as well. If a trash bag is completely compacted, it could weigh fifty pounds or more, making it difficult to handle. Many compactors use charcoal or fragrances to mask odor. Some people may have sensitivity, and it also adds another item to what you are placing in a landfill, especially the chemicals.
So perhaps you are better off without an industrial trash compactor, especially if environmental or green concerns are at the top of your list of interests.