I would argue that the British system of government is somewhat more democratic while the system in the United States is more republican.
The British system is more democratic in that it allows for more direct control of the government by the people. There is, in essence, only one branch of British government that holds the bulk of the power in that system. The legislative branch holds much more power than it does in the US where separation of powers limits what the legislature can do.
In addition to this lack of separation of powers between branches, there is less separation of powers within the legislative branch. The House of Commons holds essentially all the power. This is unlike the US, where the Senate and House act as checks upon one another.
The UK's system has many fewer hurdles built in to prevent its government from acting in accordance with the will of the people. For that reason, it is more democratic and the United States' system is more republican.