The economy of the 1930s was in the Great Depression, so called because we have never had one like it. Our economy before the New Deal was in place was pretty much unregulated, so there were no controls over how far it could fall before government stepped in, unlike today where the government is pretty heavily involved in the economy, interest rates, inflation, government contracts, the stock market, etc.
The biggest difference between the 1930s and now is the degree of government involvement we now have in the economy. In those days, the government pretty much stayed out of economic stuff -- no welfare, no social security, no Medicare, etc. The economy was pretty much left to run on its own.
Nowadays, the government is much more involved in our economy and we expect it to make sure that our economy is going well. You can see that from the way in which the government stepped in after the stock market crash and credit crunch that caused the current recession.
The greatest difference between the economy of the 1930s and the current one is that there are more governmental safeguards and initiatives in place to ensure that the elements of the past are not repeated in the same and forceful manner. An example of this would be the FDIC, which was not established in the time of the Great Depression. This meant that when banks went insolvent, individual investors had no recourse and felt the full impact of this loss with an intensity and magnitude that was both unprecedented and unable to overcome. Another primary difference is that the 1930s is used as the modern benchmark of "how bad things can get." This means that the modern crisis will always have a frame of reference which differentiates it from the past. Another elemental difference between both economic settings is that America is not as isolated with the world as it was in the early part of the 20th century. The globalization and interdependence of American within and upon the world economies marks a significant difference between both economic time frames.
The economy was very simple back then. Now people constantly engage in stock trading and there are now new policies like Medicare and welfare.
Since the question raised refers specifically to 1930's, rather than a a more general statement like "in the past" or "in first half of 20th century", i believe the reference is being made to the difference between the the worldwide economic depression of early 1930's and the current one.
The biggest difference between the economic situation then and now is that the depression of 1930's was much more severe. The current depression is described the worst since 1930's but still it is much less severe than that. Another major difference between then and now is in the way government is intervening to handle the crises. At that time the general opinion among people, government and expert was less in favour of government intervention. Also at that time the implication of a crises like that and effective was of dealing with it were not understoodd as well as these are now. As a result the government action to deal with the crisis was rather slow. IN comparison the government stepped in quite fast to offer relief in the crisis. It appears with this kind of government, the economy has already started recovering. In contrast the it took a very long time for economy to recover from the earlier crisis.