I would guess it was a mixture of both. To them, even the slightest little thing was a sign from the Gods. To them, the Gods were right there with them, in every aspect of life. There was no escaping them, or them leaving whichever spin you want to put on that the gods were always there.
I believe there was definitely an element of fear there, as you can see by the accounts of plagues and floods and anything else being taken as signs that the Gods were angry. But there was also a healthier respect shown in many of their traditions.