The major factor that can be used to compare these two eras is the extent to which there is economic inequality that comes out of the nature of business in America. In the Gilded Age, factory owners made huge amounts of money while an oversupply of low-skill workers created a situation in which the workers made very little money. This is replicated today to some extent as "knowledge workers" can make a great deal of money while those who do low-skill jobs do not get paid well because of competition both from foreign countries and from all the other people in the US who lack the skills to make big money.
The main difference between the two eras is that politics today is much cleaner than it was in the Gilded Age. While people claim that government is controlled by big businesses today, it is a much less direct form of control (if it exists) than there was in the Gilded Age. In the Gilded Age, there was much more clear-cut corruption in which government officials were "bought" by the big corporations. This does not exist in today's world where the media is always ready to expose any such dealings.