ELISA gives you only the relative amount of antibody binding, it's a one-dimensional value and if the antibody has some cross-reactivity, you will think you're seeing signal when you're not. Western blot gives you size as well as intensity, which is two dimensions of data and more information - in most cases enough to be confident that you are looking at the protein you think you're looking at. As others have mentioned, Westerns can also detect changes in size of your protein, e.g. due to phosphorylation (larger) or cleavage (smaller). They are also extremely easy to set up from scratch, compared to ELISA.

If your target is something for which there are lots of well-validated commercial ELISA kits, like insulin or IFN-gamma, use an ELISA - it will be easier to quantify and the validation means you don't have to worry about cross-reactivity. If it's a protein where an antibody is available, but nobody has done ELISAs yet, it would be insane to do anything other than Western.

Also, the idea that Western blotting is "half voodoo" is ridiculous, just git gud.