To some extent, I would say yes. In both cases, the collapses were caused by "bubbles" in the economy. These are times when the price of something gets way higher than it ought to be. People put lots of money into buying that particular thing and then when the price collapses, they lose their money.
In the Great Depression, the major bubble was in stock prices. These went up more than they should have and lots of people put a lot of money into buying stocks.
In the recent crisis, the major bubble was in housing. People paid too much for houses and then the banks and such paid too much for the mortgages.
In both cases, when the price of the good (stocks or houses) collapsed, people lost lots of money.
In a way it can be said that they were similar. Prior to the great depression also banks adopted a policy of lending money without actually ascertaining the capacity of the borrower to repay back the loans. The loans were used to speculate on the stock markets. People drove the prices of the stock of firms to record highs with no thought given to their financial conditions. A bubble was created and when it burst billions of dollars were lost within a few days.
A major cause of the present financial crisis also was the predatory lending by banks for purposes of speculating in the realty market. Banks and other financial institutions had found ways to get rid of the huge risks they were taking on through exotic financial instruments like collateralized debt obligations. These allowed the lenders to pass on their risks to others who bought the instruments as a means of making quick profits. Hedge funds, pension funds, and almost every other financial institution was involved in this game of speculation. When the bubbles that were created burst, it led to losses in trillions of dollars and wiped out the savings of millions of people.