Suppose that the program only needs about 1 MB of objects, but it will fill up 100 MB before performing a copying GC. In mark and sweep, you need to perform an operation for every garbage object (of which there are 99 MB), whereas with copying GC, you need only perform operations for every live object (of which there is 1 MB). Even if copying an object takes ten times as long as returning a chunk of memory to a free-list, the copying algorithm is faster. (Also, popping a free cell off a free-list is more expensive than incrementing an allocation pointer.) Of course, either way, the total work done for allocating objects and freeing them is O([number of objects allocated]).
Something like this is described in detail here: "Garbage Collection Can Be Faster Than Stack Allocation", Andrew Appel: http://www.cs.princeton.edu/~appel/papers/45.ps