What are the advantages of symlinks over hard links and viceversa?

This has been discussed in some detail on ServerFault.

A hard link traditionally shares the same file system structures (inode in unixspeak), while a soft-link is a pathname redirect.

• Hardlinks must be on the same filesystem, softlinks can cross filesystems.
• Hardlinked files stay linked even if you move either of them (unless you move one to another file system triggering the copy-and-delete mechanism). Softlinked files break if you move the target (original), and sometimes when you move the link (Did you use an absolute or relative path? Is it still valid?).
• Hardlinked files are co-equal, while the original is special in softlinks, and deleting the original deletes the data. The data does not go away until all hardlinks are deleted.
• Softlinks can point at any target, but most OS/filesystems disallow hardlinking directories to prevent cycles in the filesystem graph (with the exception of the . and .. entries in unix directories which are hard links).
• Softlinks can require special support from filesystem walking tools. Read up on readlink (2).

(Some details brought back to mind by mat1t. Thanks.)

Ronald wrote a hard link can have different permissions in two places. This is not right. Both places share the same inode. Permissions are bound to the inode, not the filename. So hardlinks in two places have exactly the same permissions, access times, ...