Advantages of Symbols over constants

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I wonder what are the advantages of using symbols over constants.  For
example: I want to define representation of SQL comparison operators. If
I use constants - I have to define them, but I don't have to do explicit
check when using them (because exception will be raised on non-existing
constant). It is also easy to see which operators are defined when
looking at the source code. Another advantage - constants have
namespaces: they can be defined in the class scope. If I use symbols - I
don't have to define them, but I need to verify whether the symbol is
valid. I have also to write additional documentation to indicate valid
Symbols for operators. 

I find kind of general tendency on this group to recommend using symbols
rather then constants. From what I wrote above I'd rather use constants.
Could you please explain me why should I use symbols? Am I missing some
important symbols advantage?

-- 
Marek Janukowicz