Both countries at the time would have been relatively liberal representative democracies. Even though Britain had a monarch, it was by no means a dictatorship, and even their average citizen had rights and protections. Also, in the US, slaves, women, and even the poor weren't allowed to vote. So, I was wondering, would a typical American at time be noticeably freer than when they were under British rule or compared to their counterparts in the UK? In terms of political freedom, but from a day-to-day perspective.
I'm afraid that you're somewhat mistaken: Great Britain was by no means a liberal democracy in 1787.
It wasn't until 1832 (31 years after the establishment of the UK) that the right to vote was extended from those with 40 shillings of land to those with 10£ of land, and to tenants paying 50£ of rent. It is estimated that 400,000 people could vote prior to the Reform Act of 1832, while nearly 640,000 could vote after. The UK censuses (censi?) The 1831 census in the UK showed a population of 16.54 million people so that means approximately 4% of the population was able to vote. Hardly democratic, despite parliamentary supremacy.
The Reform Act of 1867 increased enfranchisement to all make heads of household. This effectively doubled adult male enfranchisement from about a million to about two million (far short of the approximately seven million adult British males of the era. With a population of 28.9 million, only about 7% were able to vote after this reform.
There was a third Reform Act in 1884, but it's not as important. The Representation of the People Act of 1918 is where the UK truly became democratic: rights to vote were extended to all makes 21 and up, regardless of property, and to all women 30 and up with some wealth-based criteria. This act extended the franchise for men from 5.2 million to 12.9 million, and created a set of about 8.5 million female voters. This meant that nearly 48% of the population could vote (when excluding the elderly and young this number is very good.) Moreover, in 1928 votes for women were extended to all women over 21: the same criteria as men.
As you can see, the UK was hardly democratic for most of it's pre-1900 existence. The wealthy had a great deal more sway over politics than the not, and the poor were essentially shut out until the turn of the century. In fact, throughout much of the 1800s, the House of Lords held the de facto power, and it wasn't until many reforms were passed that the people came to have any say at all.
Let's talk about America.
You're right- initially in the US, many states had property laws, restricting enfranchisement to those with property. However, in 1789 Congress gave the states the right to set requirements for voting.
See, for most of the 1800s, United States was a good name for the Republic. Each state was more-or-less autonomous, and able to pass laws internally. The Federal Government acted with far less power than it does now, and as such many things are on a state-to-state basis.
Between 1792 and 1856, states began opening up to universal enfranchisement. Some states (Kentucky in 1792) extended the vote quickly, making them incredibly liberal for the era. Some (North Carolina in 1856) didn't until much later, making the conservative for the era. Some, like Pennsylvania, managed to weasel their way out of universal sufferage for men until the 1900s.
Honestly, it varies state-to-state. It is worth noting that 80% of adult, white, men could vote in the 1840 Presidential election - 2.4 million voters. Interestingly enough, the US had only about 17 million people living within them in 1840. 14% voted for the president. The UK at the same period had 15.9 million, But only a million (I'm being somewhat generous) could vote, bringing the percentage to 6.25%.
Sufferage was clearly more common in one than the other.
In 1868 the 14th Amendment to the US Constitution was passed, extending the vote to all native or naturalized citizens. In 1870 this was extended to non-whites (women were a notable exception). While this meant in theory that the voting populace had universal male sufferage, in practice it wasn't so for the African American and Native American populations, which soon were kept down by Jim Crow laws. However, it does demonstrate a high degree of political equality for poor and wealthy Americans alike (at least those that are white).
As far as women go, it varies. In Wyoming, women could vote as early as 1869. But for the rest of the country, universal female sufferage was opened up with the 19th Amendment, to all women, regardless of wealth or property. In some parts of the US, the UK was far more liberal. To poor women in the UK, the US was more liberal. In some parts of America (like Wyoming and much of the West) women had a say in politics years before their counterparts in the UK.
It wouldn't be until 1965 that all racial minorities in the US were given legal protection for their right to vote. It is a black mark on American history, and a great shame to many Americans.
However, in the 1800s,