People determine what kind of toughness they have or lack. Martial arts regardless of style are no more responsible for a persons toughness than the breakfast they eat. Martial arts are concepts and principles. They are no tangible objects that you can touch, or pick up. They are at best tools. Each persons ability, attitude, and toughness is different and unrelated to the style. They are however a product of the way their instructor trains them and how they internalize the mental aspects.

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I'm gonna go against the consensus here and say that the martial art you train will make a big difference to your mental toughness. Fact is that, no matter how dedicated to your training you are, certainly arts simply don't stretch you in certain directions.

To be more specific, personally I feel that the biggest factor in determining 'mental toughness' in martial arts is how someone deals with cardiovascular exhaustion while fighting. It's a horrible, spirit-sapping feeling and realistically you're not gonna experience it training in something like aikido or wing chun. Those arts have their own merits but making the practitioner tough and conditioned aren't amongst them imo. If this is what you want then I'd recommend a very physical art with a large competitive element like boxing, judo or muay thai.

There are no guarantees in life and toughness comes from within. It is not taught nor can it be trained. You either have to come up with it by making yourself stay the course in the face of adversity or you don't. Your question is a bit like asking which courses in college will help you become a better student.

Just anyone.

Any martial art if practiced with full dedication, mental, physical and emotional, helps in all round development(Mental toughness included). Choose any and be devoted whole heartedly.

People determine toughness, martial arts styles don't. It's all how you train and how you employ the tools. No style guarantees toughness.