If you get a PDF and a EPUB of the same document, and read it on the same device with the same version of Android, which would use up less battery power?
Theoretically ePub should have the advantage over PDF as it is a smaller file that is basially HTML, CSS and image files with a few XML files for defining the books metadata, chapter order and table of contents navigation zipped into 'ePub' format. It is in many ways like a website. The PDF files will often be larger as they have embedded fonts, image optimisation and their own encryption to deal with as overheads.
However, while ePub will reflow text easily it is not very good for more technical things like code and mathematical equations etc, so really what format to have the book in will depend on your need rather than an impact on the battery.
Also the more optimised the eBook reader the less overhead on your battery. The screen is the biggest drain on nearly all mobile devices and will consume far more battery than any eBook reader.
Conversely, an ePub with a LOT of markup and very, very large unoptimised image files could be a bigger overhead to render than a slimmed down, lower image quality PDF.
As per @Chahk 's comments below, the actual saving for a black background is quite low for an AMOLED screen where black is unpowered, and non existant on LCD based technologies. This XDA user did an experiment which should be taken as anecdotal evidence and his finding was basically after 1 hour of screen on time he had saved around 6% battery life.
How to Geek article on black wallpaper and battery which states:
On most computer displays, such as the computer screen you’re probably reading this article on, using a black background won’t save you any battery life. No matter what color a pixel is – whether it’s dark black or blinding white – there’s a backlight at the back of your screen and it’s constantly outputting light. The black pixels block more of the backlight, but it’s still behind the black pixel, using power.
EPUB uses less battery because pdf files heavy compared epubs. It also depends on what app you are using, CPU speed and RAM of device. Reading EPUB file with black background n white text saves a lot of battery.