These two pieces do not have that much in common because Hightower's is a short anecdote whereas Reagan's is a relatively long speech covering a lot of different topics. But what they both have in common is the idea that people should take care of themselves without expecting the government to help them.
Hightower extols the way that his father set up a Little League on his own rather than expecting the government to do things for him. Reagan criticizes people for relying on the government to help them out. These are two sides of the same idea -- that people should rely on themselves more.
The most telling quote from Reagan's speech is
This is the issue of this election: whether we believe in our capacity for self-government or whether we abandon the American revolution and confess that a little intellectual elite in a far-distant capitol can plan our lives for us better than we can plan them ourselves.
He is saying that the governments that are closer to the people are better. That idea implies that the people, and not the government, know best and that the people, therefore, should rely on themselves rather than building up a large government and relying on it.