Size does make a big difference to compost: once you're into the scale of many cubic metres, you get very hot, very fast composting. That will kill seeds and pathogens, and thus enable composting of a larger proportion of materials.
Communal handling also gives the opportunity for the wider distribution of low-cost high-quality compost.
So there are advantages to communal waste handling.
On the other hand, composting in your own garden will remove all the communal motorised collection and processing of waste from the equation. In most cases, that will outweigh the advantages of communal waste handling.
However, if the communal waste handling is done by very low impact vehicles, or if you've got very large amounts of organic matter that won't get broken down in a smaller compost heap, or you simply wouldn't have the space for your own compost heap, then the communal heap might just have the edge.