I don't have experience with both, but I am self taught with a great many things and I will say there is a huge time advantage for me to learn something when I have an actual teacher who can tailor education to me rather than a book or video where I have to deal with an approach that by the nature of the format has to be one size fits all.
Language in particular I have done both with, and I have found that while many methods of doing something (such as spaced repetition, trial and error, lots of practice, etc) work, a live human being instructing me has always led to me being good much quicker.
Good luck, I am only using free resources atm and not making quick progress at all with my voice, but I bet a voice coach would save me tons of trial and error.