I think parametric methods are actually exactly what you are looking for.
abstract Option_1
abstract Option_2
foo{T<:Options_1}(...) = do_something()
foo{T<:Options_2}(...) = do_something_else()
if there is common code between the two implementations then factor it out into another function and use it in both. Julia doesn't have enums but it does have ways to accomplish the same thing and parametric methods are a perfectly valid way to do so.