Both have their place.

The first type is literally how we got our understanding of irony. Characters in stories would say things that meant a lot more to the audience than it did to them in the moment. This could be used for both comedic and tragic effect. For building tension, it's less about what's around the corner and more about whether or not the character will deal with a situation that we know they're in but they're still ignorant of.

The second type is great for mystery and building tension from the unknown. As the unknown becomes known, we may find it shocking, scary, humorous, or exciting. It's also probably better for setting up major plot twists, but you can still pull off twists with the first type.

Plenty of stories will also incorporate both. For instance, a story may have a set of characters whose perspective we follow, and while following them, we really only see what they see. However, little details may be relevant to another character before they become aware of it.