Understanding One to One Relationships
1 to 1 (or possibly 0) relationships are not cross referenced, they are implemented as your 2nd example, with one of both entities related to the other one (and not the other way around).   

Linking both ways would be redundant for one of the relationships, as you just need 1 to know the nature of the link. Also, in databases that don't support deferrables foreign keys or multiple inserts in one statement (thanks to  @ypercubeᵀᴹ for this note), you won't be able to insert the rows without disabling the foreign key first.

If the existance of stuff depends on more and more depends on stuff then there is a problem of the chicken and the egg. Which one really represents the entity you are trying to store? Do you really need 2 different tables for them? Does your entity exist only when both records are created?

1 to 1 relationships always raise an eyebrow when designing. Maybe if you had a particular case scenario to share we could delve more in detail. The only few exceptions I've implemented 1 to 1 relationships are when we inherited previous databases with tables that had 100+ columns, and we split them up for performance and storage issues, but not for pure designing reasons.