Ubuntu – In terms of battery usage, which distro is more efficient between Lubuntu and Xubuntu

Your case studies are indeed challenging.

Take your Grandpa PC

Pentium 2 and 64Mb RAM.

Lubuntu minimum requirements are 128Mb if using the alternate installer - 256Mb for the Graphical installer.

The recommended RAM is 384Mb just to run the LiveCD.

Therefore - I'm afraid, you will not be able to install a graphical environment on Grandpa PC. At best you might get a text only "server" type install via a minimal ISO - i.e. you need a minimum of 64Mb to run the minimal CD.

The "old meat":

That is more promising:

Pentium 3 with 128Mb RAM - you should be able to squeeze on Lubuntu via its alternate CD.

However the minimum requirement for Xubuntu is 256Mb with 512Mb as a recommended RAM size.

I've experimented with various "low" RAM installs. I've never tried 128Mb - but in general, I install from a minimal ISO CD and install various components manually - for example, SLIM, LXDE with apt-get install --no-install-recommends to ensure no excess packages are installed.

Typical packages you should look out for if you go this route are described in the linked question below.

Stick with a lightweight browser such as midori - abiword should be ok for wordprocessing.

Flash and general movies will struggle with your video card. However playing music should be fine (see below)

Links:

1. https://help.ubuntu.com/community/Installation/MinimalCD
2. How do I install LXDE / Lubuntu?
3. Lightweight music player

Xubuntu uses the same kernel as Ubuntu, as well as the same low-level power management utilities (hdparm, etc.), so yes, it has the same power management capabilities as Ubuntu.

But, Xubuntu may be more power-efficient than Ubuntu on your laptop, primarily because it's a "lightweight" desktop environment; it places somewhat less load on both your CPU and GPU compared to Ubuntu (Unity 3D). Whether it saves power over Ubuntu (and how much) depends on your specific hardware and use patterns.