The Constitution was different from the British system of government in several ways. One way it was different is that the British have a King or Queen that isn’t elected. This person inherits the position. In our country, we have no person who inherits any government position. We elect our government leaders.
Another difference is that we have three branches of government. Each branch has a different job or responsibility. No branch of government could do everything by itself. Each branch also has the ability to control the other branches. There are no checks and balances on the King or Queen.
In our government, we emphasize that our government gets its powers from the people. The role of our government is to protect the rights of the people. The King or Queen doesn’t get his or her power from the people.
There are several ways our system under the Constitution differs from the British system of government.
Based on your question, it seems that you are referring to the late 1700s, during which time the Revolutionary War occurred (1775-1783) and the Founding Fathers of America began drafting a government. This occurred first in the form of the Articles of Confederation (beginning around 1781), and secondly in the form of the Constitution of the United States.
The biggest difference between the U.S. Constitution and the British Government at the time is that the British Government was a monarchy, led by King George III. The British also had a Parliament, comprised of a House of Lords and a House of Commons. Parliament functioned as the legislative branch. However, the bulk of the power within this system rested with King George himself. This became one of the chief complaints of the American Founding Fathers - that the executive (king) had too much power.
Therefore, during the Constitutional Convention, the Founding Fathers endeavored to create a system that spread the power across three different branches: the executive (President), legislative (Congress), and judicial (federal court system, led by the Supreme Court). Under this system, there would be "checks and balances" that prevented any one branch from exercising too much power. For instance, the President may veto (cancel) a piece of legislation (law) passed by Congress. The Congress can impeach a President. The Supreme Court interprets the constitutionality of laws, and can strike them down if necessary.
Lastly, the United States Constitution provides the people ("We the People...") with the power to elect their officials, from local representatives (House) to Senators (as a result of the 17th Amendment in ~1913), and the Presidency (through the Electoral College). In the British system, the loyal subjects didn't vote for the executive, because the monarchy was passed down through the family blood line.
This question ought probably to be rephrased. A constitution and a system of government are two separate things, so any comparison of the two will necessarily be subjective. The Constitution of the United States establishes a system of government; that system might be better compared with the British version.
Alternatively we might compare the U.S. Constitution at ratification with the constitution upon which the British system was based at that time. The most obvious difference is that the U.S. Constitution is a written document where powers are clearly defined in writing, whereas the British system of government is based on an unwritten constitution and government powers are based on established but unwritten customs.