The major similarity between a presidential democracy and a parliamentary democracy is that both of these types of governments are democracies. This is a fundamental similarity that is, perhaps, more important than any differences. Both of these forms of democracy allow people to vote for their leaders. This makes them superior to other forms of government that do not allow their people to enjoy popular sovereignty.
However, there are important differences between the two forms of democracy. First, a parliamentary democracy is less likely to encounter gridlock than a presidential democracy is. In a parliamentary system, there cannot be a situation in which the chief executive is from one party while the legislature is (in whole or in part) controlled by a different party. This makes the parliamentary system more efficient. Second, a presidential system allows for separation of powers where a parliamentary system does not. In a presidential system, there is a clear distinction between the legislative and the executive branches of government.
Thus, these two types of government are similar in the most important way. However, a parliamentary system is more likely to be efficient while a presidential system allows for separation of powers and, thereby, greater protection of people’s rights.