Each of those pairs you present sound equally correct out of context (though in one case one is a familiar quote), but in each pair the examples have different semantics and each would sound better in different specific contexts (and sometimes they would sound equally correct even in context but have slightly different meaning, at least in connotation.)
Many languages express the verb "to fear" as "to have fear" (tener miedo, avoir peur) so to insert an article ("I have a fear" ...") becomes almost psychologically problematic, it's "unlearning" plus learning.
