I would add to this that using client memory to store your vertices is potentially more detrimental to performance than the number of draw calls. The reason for this is that if GL does not have full control over the vertex memory it has to either make a copy of your vertex array every time you draw or synchronize the pipeline (e.g.
glDrawArrays (...) will not return until GL finishes using the data). When you use VBOs, GL manages the memory and it knows when the data changes so
glDrawArrays (...) can safely be implemented asynchronously / without making an immediate data copy. Hundreds of draw calls using VBO-managed memory can be quicker than a handful of client memory draw calls as a result.
For this reason, immediate mode (which creates new vertex data each time it draws) can actually be more efficient in certain circumstances than using vertex arrays. Granted, using client memory to store vertex arrays has been deprecated for many years as has immediate mode, but since you brought up the fixed-function pipeline it was worth mentioning.
On the DirectX end of things, prior to Windows Vista issuing a draw call would invoke an expensive kernel-mode context switch. This was never an issue in OpenGL, because it always had a user-mode component to its driver, but D3D only gained a user-mode front-end with the introduction of WDDM. D3D10 also shifts the responsibility of resource validation from usage to load-time, so draw calls are even less expensive when you move from D3D9 to D3D10.