Hamilton participated in the formation of the US as a Federation, so we are talking about the first US Senate.
A very distinctive feature is transparency. At that first moment, the meetings were secret, there was no permission from spectators and for a long time did not even have the publication of minutes. Today, with Democracy consolidated, there is transparency. Everything that happens in the Senate is documented and transmitted to society through official media and the press.
In addition, the role of the vice president of the republic should be emphasized. In that Senate, the vice president had the power to command the Senate. Today, the vice president only fulfills his missions in executive power, while the president of the Senate is chosen by a vote among the senators.