D3DX is more analogous to GLU. The functionality provided by each library may differ, but the underlying intent is much the same. So you'll find routines for quadrics, tesselation, some limited matrix work, some helpers for texture loading in GLU, and you'll find a whole bunch of other routines in D3DX, some of which overlap, but in both cases they supplement the core API (by wrapping functionality, by providing some handy helper routines, or by providing an implementation of some things that you would otherwise need to write code for yourself) rather than being an actual part of it. It's perfectly possible to write a GL program without even touching GLU and it's perfectly possible to write a D3D program without even touching D3DX.
Re: drawing lines - both OpenGL and D3D provide support for lines (lines are even still a core primitive topology type in D3D11), but the problem may occur when you talk about lines wider than 1 pixel, which may or may not be supported in hardware by consumer cards.