The term Anthropocene is used to describe this as an era in which human activity in general is the driving force behind climate change. It is best characterized, IMHO, by the Al Gore focus on saving the climate by getting ordinary humans to make adjustments in their consumption habits-most famously, his push for people to switcht the type of lightbulbs being used. It calls for no major changes in the structure of the economy or of society, tends to be a "top-down" perspective, and can probably be traced back to Puritan notions about the sinful nature of man. It tends to be the label used by "liberal" or "moderate" political figures and those in the mainstream environmental leadership, since it exempts their large donors from any real responsibility for the situation and asks nothing of anyone but the proles.
The term Capitalocene, on the other hand, is used to push for the idea that the driving force of climate change is corporate arrogance, recklessness and greed. It situates blame for the crisis in the capitalist system(and, to a lesser degree, to the industrialist, resource-extraction based economies most countries have embraced, regardless of their stated economic structure) since the dawn of the Industrial Revolution.
Which of these terms are you more likely to use, and which of these do you feel is a more useful label for the current crisis? Do you believe that it's possible to avoid climate catastrophe strictly or mainly through the human race in general making personal efforts to reduce our individual carbon "footprints", or are you among those who think only radical structural change can save us from disaster?