Both. And it is in two ways here: anger and aversion directed towards beings and anger and aversion directed towards the way things are. Anger and aversion directed towards beings or people can be dealt with skillfully through practicing Compassion, supported by Equanimity. Compassion without Equanimity can easily fall into grief and, if it is idealistic, into aversion. If we care too much, we may become idealistic and not understand what we have the power to change and what we don't have the power to change.
As far as anger and aversion directed towards the way things are, it is usually Equanimity that overcomes this. Sometimes when someone is doing something difficult, we may be able to reflect and develop more Compassion and have Patience with that, but sometimes it is difficult to have Patience with the way things are because we feel frustrated by our inability to change things or to control the way things are. So when we experience anger or aversion towards impermanence, towards the fact that Dukkha even exists, the fact that we do have a limited ability to control things, we have to fall back on the power of Equanimity based in Wisdom to overcome it. And that actually is based in Compassion for ourselves.
So it is both, Compassion and Equanimity. But, certainly, with beings it tends to be more of a focus on Compassion supported by Equanimity, while, on the other hand, with the impersonal Dukkha of existence it seems to be more of Equanimity supported by Compassion for ourselves.