Chemically speaking, synthesized vanillin is indistinguishable from the vanillin extracted from plants.

But vanilla plants contain a lot of other flavor/odor chemicals (like anise alcohol/methylguaiacol, p-hydroxybenzaldehyde/trimethylpirazine, p-cresol/anisole, guaiacol, piperonal) in addition to the one primarily chemical (vanillin), which may also be desirable in certain applications, such as foods or perfumes.

I would have no problem buying 750 mL of 40% grain alcohol loaded up with sugar and artificial vanillin if I'm gearing up for a giant bake sale or something, but I'd still keep the 10 mL bottle of the real stuff for finishing sauces, frostings, icings, or beverages.

Important caveat, though: vanillin derived from engineered bacteria or yeasts may be eligible to be labeled as "natural flavor"!