Which is faster, the List<T>.Remove(T) or List<T>.RemoveAt(int) method?

Simple answer:

In general, RemoveAt is quicker, though not always hugely.

Long answer:

Let's just consider finding the appropiate item first. The Remove method has to search the list for the item that matches the given object, and is thus O(n) time in general. RemoveAt on a list can simply index the given item, and is thus O(1).

Now, removing an item from the end of a list is always O(1) of course, but in general removing an item takes O(n) time, because reshuffling needs to be done (moving items after the removed one forward). Therefore, in the general case, the total time complexity for removal is either O(n) + O(n) or O(n) + O(1) for Remove and RemoveAt respectively, hence simply O(n) in either case. However, RemoveAt is guaranteed to be at least as quick, though scaling is the same unless you know you're removing it at/near the end.

List.Remove(T) uses IndexOf and RemoveAt(int) in its implementation. So List.RemoveAt(int) is faster.

public bool Remove(T item)
{
    int index = this.IndexOf(item);
    if (index >= 0)
    {
        this.RemoveAt(index);
        return true;
    }
    return false;
}