The 1920s was a time of excess in nearly every way; following the war, all restraint was gone. That was true in personal morals and behaviors as well as economic practices. They had it, they spent it, and they invested it, but they didn't save it. Same goes for the modern era you mention--life is good and money appears to be plentiful, and we spent rather than saved.
I think that the government has learned that the Federal Reserve has to step in and try to help control the rise in inflation. They try to do this by controlling the interest rates that are charged.
Our economy in the 1920s was much, much smaller than today's is, and much less resilient and flexible. There was not nearly the amount of capital and wealth in the country at the time nor anywhere near the infrastructure system we have. The lesson we should have learned that applies in both time periods is that deregulation (or non-existent regulation as in the 1920s) may lead to short term gains, but in the long run can severely damage an economy, especially for the lower economic classes.
I think the main lesson that investors should have learned is to beware of bubbles. That was similar between the 1920s and the 2000s -- there were bubbles that led to overpriced assets. The problem is, however, that it's hard to tell when something is a bubble and when it is not. So it's not as if it was a really obvious lesson that any idiot could have learned and applied to the situation a few years ago.