There's no hard and fast rules on which to use. To summarize:
Opacity Pros:
- Allows animation
Display Pros:
- Hidden removes it from mouse handling
- Improved accessibility when hidden
- Shows state in timeline (but you still need two keyframes to animate)
You can also technically use both -- animate opacity over time and then also use the display to remove from accessibility. This is usually overkill though.
Personally I just use Opacity a lot, but I think that's more a force of habit since Opacity has been in Hype since v1.0 and Display came later (~v3.6 I think).