The small one will redistribute my money where I live at least.

Besides, there is an alternative model where there are competing groups of people and I can pick the best among them based on price and services.

In the absence of government, what's stopping these groups from simply joining forces into a cartel, getting some armed thugs and making you an offer you can't refuse? History suggests that to be a far more likely scenario. Oligarchy, rather than competition, is the natural state of capitalism.