The Allies had different goals of victory for the end of the war, so a discussion of conditional surrender has to take this into account. Churchill, coming from a more traditional British school of thought, was primarily focused on restoring the old European balance of powers system of international governance which relied on equilibrium. It would have seemed natural and logical to allow the Germans to negotiate a conditional surrender on the Western front while rebuilding the Western world (including Germany) to balance the ever growing Soviet Union. However, President Roosevelt had a colliding viewpoint. He instead imagined a 'new' world order, one that was based upon international harmony and cooperation rather than the somewhat anarchic balance of powers system. Kissinger quotes the US Secretary of State:
...there will no longer be need for spheres of influence, for allies, for balance of power, or any other of the special arrangements through which, in the unhappy past, the nations strove to safeguard their security or to promote their interests.
The balance of power and the new world order were in direct conflict with each other, and, as mentioned in /u/orincoro's comment, Churchill did not want to 'push his luck' with the American aid he was now dependant upon. Even in 1944, before the Americans had landed, Roosevelt was already expressing ideas associated with American isolationism, and regretting that America had to come to the aid of Europe:
As I suggested before, I denounce and protest the paternity of Belgium, France and Italy. You really ought to bring up and discipline your own children. In view of the fact that they may be your bulwark in future days, you should at least pay for their schooling now!
Statements like these would have been extremely worrying to Churchill, who at this point was the head of a tired British war effort. He simply could not risk pressuring Roosevelt too hard at the risk of losing the war. In order for Roosevelt's vision of the Four Policemen to come to fruition, a complete removal of Hitler and disarmament of Germany was required. This put an enormous emphasis on an unconditional surrender from Nazi Germany.
Stalin's peace goals were instead based entirely on Realpolitik. The more land Stalin could acquire, the larger the security-belt or buffer zone would be to protect Russia. Roosevelt's unconditional surrender proposal was therefore very appealing since it would remove the Axis from peace negotiations entirely, allowing for a great deal of flexibility and exploitation at the negotiating table for Stalin.
Kissinger, Henry. "Three Approaches to Peace: Roosevelt, Stalin, and Churchill in World War II" in Diplomacy. New York: Simon & Schuster, 1994.