Besides differences in government response, the other big difference was that employment had become more secure, more long-term, more Henry Ford and less Charles Dickens. You could indeed argue that this made it more serious. Compare a 20% drop in employment which meant 4 days a week for everyone (because they were all casual, factory or farm) vs 1/5 of workers (who thought they had jobs for life) being unemployed for years.
I am not claiming nothing of this. But everyone knows the huge toil of the great depression on poor workers. The only reason why the new deal was enacted is that people were on the verge of revolt. If the recession had been any worse, there would be blood on the streets and even more people would starve to death, and possibly the US government would be overthrow by communists who were very active at the time. That's the fundamental reason why these silly ideas pushed by conservatives never come to fruition: a completely free market is guaranteed to lead to revolution sooner or later.
I'm just dubious of claims that it was economically a great idea, especially in the long run. This seems to be unclear from the data, looking back from a safe distance.
Actually the USA in 1910 was the richest society the planet had ever seen. This was why half of Europe was busy trying to move there, to start at the bottom. (It was poor by today's standards, of course.) It's a lie to claim they got rich "because of socialist policies".
The depression was a brief dip in the growth of the income of the average guy, over let's say 1870-1970. Things went backwards by the equivalent of about 15 years or progress (on average! it was rough for some). The effect of the new deal on ending this, or perhaps prolonging it, is a confusing issue. Certainly it paid some people's wages, and hit some rich people hard (and had non-economic implications too), but my understanding is that there's a serious argument that, without such action, the depression might have been sharper & shorter, like the 19th C ones.