The difference is negligible and irrelevant. Creating a hard link or a symbolic link only takes up a few bytes. A hard link costs one directory entry: space to store the name and the inode number in the directory. A symbolic link also costs one directory entry, plus space to store some metadata about the symbolic link; depending on the filesystem, this information can be stored in the directory entry or require a separate inode. A symbolic link uses a few more bytes, around the order of 100 or so, which is negligible — less than 1/1000 of the files you're storing.
If you had very small files, and you had so many files and so many links per target that adding hundreds bytes per target was relevant, then a proper database would be more appropriate to store your data. But to make links just to classify files, that's irrelevant.
Disk usage tools won't tell you the size consumed by an extra hard link or symbolic link because they only show the size of the file content, not of the metadata, and a symlink is all metadata, as is an extra hard link to an existing file. (Technically, the “size of a hard link” is the size of the file. After all, every file that has a name has a hard link, and the content is the same regardless of whether there is a single hard link or more.) Beware that some unsophisticated tools may count the size of a file twice if they see it from different paths;
du and most graphical file managers do count files only once.
Usually symbolic links are easier to manipulate. They let you clearly identify which is the original and which is the target, whereas with hard links, all the names are equivalent. Another point about symbolic links is that if you edit the original, the symbolic links aren't affected, whereas editing a file that has multiple hard links may break the links, depending on how the editor works (overwrite with the new version vs. write a new file and move it into place).
If you want to be able to move files around in the primary classification, then you need to use hard links, because symbolic links are purely textual, they don't follow their target around.