In NLOpt, with constrained gradient-based optimization, should I use equality constraints or inequality constraints?

Question

It seems like quite often, either one could apply. That is, I have some function which I know has a minimum of 0 and I want to specify that it has to equal 0. Does it make more sense to specify a constraint f(x) <= 0 or f(x) == 0?

My guess is I should use equality constraints since this feels suspiciously similar to modeling an equality constraint by adding an inequality constraint on both sides to get an equality constraint (f(x) <= 0 and also -f(x) <= 0) which apparently doesn't generally work for some reason.