I did some battery testing on various distros a while back, what I found was that most were pretty similar. Despite being "lite" or low resource" they rarely did much better than Ubuntu or Mint with Cinnamon (which are actually quite well optimized). These numbers are a couple months old, I no longer even have the laptop so please do not ask for more tests.
Method:
Tests were done using TOP which isn't a perfect way to get accurate numbers, but I did run the tests 3 times for consistency so numbers may not match real world numbers 1 for 1, they do still tell a tale.
Warning:
If you are going to read this, please read my comments as well, if you only look at the data itself, you will get an incomplete view and draw some incorrect conclusions. The summary at the end is especially important.
TL:DR Read the summary at the bottom
System:
Lenovo X220, 2nd gen Core I5, 16gb ram(?), stock 320 hard dive, bluetooth, with IPS screen
Windows 8.1 @ minimum brighness
Out of the box 10 watts
Lenovo Power management brought it down to 9.8 watts
With an SSD and heavy tweaking I got it down to 6.8 watts.
Out of box wattage use with no power optimizations…
LXDE (low power Ubuntu) - - - - - - - - - 11.3 (I think this was Lubuntu)
Apricity with Cinnamon (Arch distro) - - 11.3
Mint Cinnamon - - - - - - - - - - - - - - - - - -12.3
With TLP and Intel Pstate
LXDE - - - - - - - - - - - - - - - - - - - - - - - - - 11.6 (actually went up!)
Apricity - - - - - - - - - - - - - - - - - - - - - - - - 11.3 (change was within what I considered margin of error)
Mint Cinnamon - - - - - - - - - - - - - - - - - - 9.95 (largest drop)
With more tweaking and an SSD I got Mint down to 6.8, putting it on par with Windows 8.1
Yes, these are idle numbers, however, real world use the battery life was about 90% of Windows 8.1, which is rare in a Linux laptop, a bit more tuning and I bet I could get it even closer. On the stock 6 cell battery, I could get between 4 and 5 hours, and with the extended 9 cell I could almost reach 9 hours. Remember, this is a 5 year old laptop that weighs under 3 pounds and has a full power I5 processor, not a U series. It can hold its own with modern U series processors. For a total investment of about $300, it's a cheap, workhorse Linux machine.
Strangely, Intel pstate loves PCs and hates Macs, I think usage of it actually interferes with the internal power management or something. Basically if you want to run Linux on mac, research as it's just not quite the same as on a PC and what you do can backfire.
Notes on Peripherals
Sdcard used 0.1 watts
Bluetooth consumed less than 0.1 watt
Logitech Unifying Receiver (older model) 0.5 watt (I have yet to test the newer micro versioon)
This kind of shocked me. I expected bluetooth to be almost on par with the receiver.
Advice, use Bluetooth instead of a receiver!
Various distro info
Distro - - boot time min/sec - - - - % cpu at idle - - - - memory at idle
Mate - - - - - 1:23 - - - - - - - - - - - - - - 0-0.1 - - - - - - - - - - - 7.3%
XFCE - - - - -1:13 - - - - - - - - - - - - - - 0-0.7 - - - - - - - - - - - 11.8%
LXQT - - - - -1:50 - - - - - - - - - - - - - - 0-0.7 - - - - - - - - - - - 15%
Manjaro Arch Linux distros
KDE - - - - - - 0:21 - - - - - - - - - - - - - - 0.7-2.0 - - - - - - - - - 12.7% (very fast for some reason)
Cinnamon - 0:22 - - - - - - - - - - - - - - - 2-2.5 - - - - - - - - - - 14.7% (Before installing all updates)
Cinnamon - 1:34 - - - - - - - - - - - - - - 1.4-2.3 - - - - - - - - - - 14.7% (not sure why the huge change after updates, CPU load dropped, boot time increased)
Budgie - - - 1:32 - - - - - - - - - - - - - - 0.7-2.0 - - - - - - - - - 12.7% (didn't see if there was a difference before vs after updates)
Nope, not typos!
These numbers are all over the place, however idle is not where you drain your battery, it's when you are under load. So what's the point of these numbers? To prove that they are all over the place and that you shouldn't assume anything.
Regarding memory... You want to use it to make the system fast and efficient, so don't assume it using more ram is a bad thing. By this I mean if using 3% more ram for the system results in a 10% speed increase on every app you run, that's a good tradeoff, whereas if lowering system memory use by 2% causes every app to run 10% slower, did you really make it more efficient? How it's used is far more important than how much is used, however a lot of people equate using more as instantly meaning less efficient and it's simply not true.
Note regarding Manjaro: Despite saying not to assume anything, I can assure you, a true Arch install with Cinnamon would run better/more consistent than Manjaro did here (If you did it right!). I used Manjaro because it made for an easy way to test various desktop environments on Arch quickly and I thought consistently, however, it's obvious not all are created equal. This is not meant to criticize or disparage Manjaro or its users, these are just the numbers I recorded at the time. It's a good way to try Arch, which can be a bear to install, and may have just been a fluke. Regardless, if you love it, by all means keep using it.
Summary, so what does this all mean?
While these do give an indication as to how efficient the underlying OS runs, they tell a very incomplete story, the reason for that is optimization. Looking at these numbers you would think that Mate or another older environment would be the lightest to use, and that's true, at idle and if you're building a file server, it makes a great choice. Where things get dicey is when you need to render something like a web page or video, at which newer protocols and optimizations actually make Gnome3 and the like more efficient, IF you have a newer processor that supports them.
My advice, if you have and an older system such as an Atom powered netbook or a VM without VT, sure, use Mate or LXDE. the processor is too old and slow to really take advantage of newer protocols and optimizations so it's going to use extra cpu to browse and watch video. However, if you have a newer processor/video card, use a newer desktop environment and take advantage of those optimizations as they can actually consume less battery than those older environments when doing more cpu intensive tasks.