There are two major differences between these two legislatures.
First, Congress is truly bicameral whereas Parliament is not. In Congress, both the House of Representatives and the Senate must agree in order for a law to pass. The House of Lords, by contrast, cannot block bills except in very limited circumstances.
Second, Congress has no real part in the executive function of the US government. Congress is a legislative body and is separate from the executive. The British Parliament, on the other hand, is an integral part of the executive branch. The government’s ministers, including the Prime Minister, come from the Parliament and remain as members of Parliament even as they act as leaders of the executive branch.
In these ways, Congress embodies the American system of separation of powers while the British Parliament does not.
The differences between the British Parliament and the U.S. Congress are substantial. The British system of government provides much greater power to the majority party than exists in the American system of government. In the United States, presidents are elected independent from congressional elections, and serve independent from the legislative branch of government. The U.S. Constitution independently establishes each of the three branches of government with the intent that no one branch can exercise undue levels of influence in the running of the federal government. The president can, then, represent a political party different from the majority parties in the two houses of Congress. In Britain, the prime minister is elected from among the majority party in the House of Commons, the main legislative institution in that country, the House of Lords being more ceremonial. Whatever political party constitutes the majority in Parliament selects the prime minister. The prime minister, in turn, selects his or her cabinet officials from within his or her party's membership in Parliament. In other words, there is no real separation of powers there.
The U.S. Congress, per the Constitution, has two chambers both of which wield considerable power and the composition of which is entirely separate from the other. One political party can hold the majority in the House of Representatives while another party can hold the majority in the Senate. The two chambers have overlapping responsibilities but distinctly different levels of authority. The House, for instance, is vested with responsibility for originating spending bills, and the Senate alone confirms presidential nominations to high-level positions in federal agencies (e.g., the Departments of State, Defense, Treasury, etc.). The Senate, in addition, is the sole legislative body vested with authority to ratify treaties entered into by presidents.
These, then, are the major distinctions between the British Parliament and the U.S. Congress.