In The Presidential Character, James D. Barber analyzed US presidents according to two criteria: whether they were active or passive in their approach to the office and whether they regarded it in positive or negative terms. According to this analysis, presidents fell into one of four essential types: passive-positive, passive-negative, active-positive, and active-negative.
Passive-positive presidents tend to be genial and likeable and are often popular with the American people but can lack the courage to make politically unpopular decisions. Examples include William Howard Taft and Ronald Reagan.
Passive-negative presidents are those who regard the presidency as a burden which they assume from a sense of duty. They do not enjoy it and are glad to give it up. Examples include Calvin Coolidge and Dwight D. Eisenhower.
Active-positive Presidents are exuberant and enthusiastic about the presidency, relishing the challenge of the office. Examples include Theodore Roosevelt and Franklin D. Roosevelt.
Active-negative presidents are power-hungry, inflexible, and dictatorial. Barber says that they are the most dangerous category and have "a strong bent for digging their own graves." Examples include Lyndon Johnson and Richard Nixon.
The ideal personality for the president depends to some extent on the circumstances of the presidency. An active-positive president is probably most suitable for times of crisis. In times of peace and prosperity, one could make a case for either a passive-positive or a passive-negative president. The former will probably be more popular but the latter is less open to corruption, being actuated by a sense of public duty.
It is quite clear, given the above categories, that Barack Obama was a passive-positive president and Donald Trump is the exact opposite, an active-negative president. Barber says that passive-positive presidents "help soften the harsh edges of politics" by coalition-building, which was always Obama's approach. However, this means that they are in danger of being led into policies in which they do not truly believe (such as Obama's foreign policy in the Middle East) or abandoning objectives (such as closing Guantanamo Bay).
Active-negative President's, in sharp contrast, are authoritarian and fail to take account of the views of others. This fits in with President Trump's tendency to release information via Twitter rather than using official channels and the high turnover of government officials and White House staff in his administration.