At the time of the Constitution’s ratification, our government was as close to the Roman Republic as it would ever be. And then things began to change as we moved in the direction of a democracy. The property qualification was steadily reduced until about 1850 when it was removed completely; the electors came to be chosen by the people instead of the state legislatures, giving the people a direct say in electing the president; and finally, in 1910, the law for electing senators was changed to allow the people to elect them directly.
The differences between the two Republics was dictated by the difference in culture and time, but our attraction to the ancient system because it had no monarch led us to the creation of a new version designed to withstand the modern age.