TL;DR The Facebook and Messenger apps are battery hogs. Replace them if possible.
I'll start by saying these experiments aren't highly scientific, but I tried to be as consistent as possible.
For each iteration, I tested from 100% charge to 97% charge. I wanted to test more than 1% because my phone seems to go from 100 to 99 relatively fast, but 99 to 98 much slower. I figure spreading the average across more percentage points would increase accuracy, but at the same time, I didn't want to spend days on this experiment. I am on wifi, and have terrible mobile signal, so, for consistency, I kept the phone in the same spot on my desk the whole time. The only way I thought I could be as repetitive as possible across tests is to not use the phone. The biggest harm to battery life is anything that interrupts "deep sleep" mode on the phone, so with these short 3% tests, I wanted to try and maximize the time the phone would have the chance to go into deep sleep. While you're actively using your phone, you're unlikely to see the same battery performance as these tests, but the relative improvement should still be noticable.
For test #1, I have the full apps installed. In fact, these apps are pre-installed on my Galaxy S10+ phone (more on that later). They have been updated via the play store, but are otherwise the official Facebook provided apps.
Starting at 100% battery, 22.5 minutes later, I hit 97%. 3% in 22.5 minutes. 22.5/3 = 7.5, so 1% every 7.5 minutes (averaged).
Facebook provides "lite" versions of both of these apps, so I wanted to experiment to see how those perform. The usage experience is subtly different, but adequate enough for me. If the battery improves, the trade-off to lite apps is well worth it.
Starting at 100% battery, 54 minutes later, I hit 97%. 54/3 = 18, so 1% every 18 minutes (averaged).
Much better!!! that's a 2.4x increase in battery life.
In the play store, there is an app called "Hermit" which is basically a browser that will appify mobile sites, block ads and malware, and give you a dedicated icon for your app on the home screen. It comes with some ready-made apps that you can start with, including Facebook, and Messenger. It integrates with Android nicely, and still allows you to share things to Facebook or Messenger.
It has lots of other benefits like "Full Screen" mode and "Dark" mode, but I won't get into that here.
For this experiment, I removed Facebook Lite (but left Messenger Lite) and installed Hermit. I logged in to Facebook using Hermit, and added the Facebook icon to my home screen to keep it convenient.
Starting at 100% battery, 92 minutes later, I hit 97%. (!!!) 92/3 = 30.666666667, so 1% every 30ish minutes (averaged).
Wow!!! That's a 1.7x increase over using the lite app, and 4x increase over using the default app.
What happens if we put Messenger into Hermit also? This time, I removed Messenger Lite, and used the ready-made Messenger app in Hermit, logging in, and adding it to my home screen.
Starting at 100% battery, ** 96 minutes later**, I hit 97%. 96/3 = 32, so 1% every 32 minutes (averaged).
So it looks like Messenger Lite isn't much of a drain on the battery, but I'll still keep it in Hermit just so I can have Dark Mode. :)
I think it's important to understand that, even though I am reporting percentages and minutes, you should think of it all in relative terms. Your battery size may be different, app usage will be different, deep-sleep time will be different, and the apps you have loaded will be different. But, it's clear that removing Facebook helps battery life, and depending on your preferences, the Lite versions of Facebook and Messenger, or using a different browser app, like Hermit, might give you just as good of an experience, while substantially increasing your battery life. You might not see the same minutes, or the same multiple, but you should see a relative increase in battery life, no matter what.
What about iOS?
Well, I have no idea... I didn't test iOS. That said, you can do your own experiment by removing Facebook (there is no mobile web view for Messenger), then go to the mobile site at m.facebook.com and add a shortcut to your home screen. Let me know how it turns out!
Footnote:
How did I uninstall the pre-installed Facebook apps?
Prerequisite: You need to know how to use ADB. Root is not required.
I uninstalled Facebook, and other built-in apps using adb shell:
adb shell
pm uninstall --user 0 com.facebook.services
pm uninstall --user 0 com.facebook.katana
pm uninstall --user 0 com.facebook.system
pm uninstall --user 0 com.facebook.appmanager
pm uninstall --user 0 com.facebook.orca
exit
I also have removed some of the other pre-installed apps and services, not related to Facebook: (Don't remove apps you actually use)
pm uninstall --user 0 com.samsung.android.bixby.wakeup
pm uninstall --user 0 com.samsung.android.bixby.service
pm uninstall --user 0 com.samsung.android.bixby.agent
pm uninstall --user 0 com.samsung.android.bixby.agent.dummy
pm uninstall --user 0 com.samsung.android.bixbyvision.framework
pm uninstall --user 0 flipboard.boxer.app
pm uninstall --user 0 com.samsung.android.wellbeing
pm uninstall --user 0 com.samsung.android.email.provider
pm uninstall --user 0 com.wsomacp
pm uninstall --user 0 com.sec.android.app.sbrowser
pm uninstall --user 0 com.samsung.android.app.sbrowseredge
pm uninstall --user 0 com.samsung.android.hmt.vrsvc
pm uninstall --user 0 com.samsung.android.app.vrsetupwizardstub
pm uninstall --user 0 com.samsung.android.hmt.vrshell
pm uninstall --user 0 com.google.vr.vrcore
pm uninstall --user 0 com.samsung.android.kidsinstaller
pm uninstall --user 0 com.samsung.android.app.camera.sticker.facearavatar.preload
pm uninstall --user 0 com.samsung.android.app.ledbackcover
pm uninstall --user 0 com.sec.android.cover.ledcover
pm uninstall --user 0 com.sec.android.cover.ledcover
pm uninstall --user 0 samsung.android.app.cocktailbarservice # android 9 only
pm uninstall --user 0 samsung.android.aremoji
pm uninstall --user 0 samsung.android.emojiupdater
pm uninstall --user 0 com.samsung.android.app.cocktailbarservice # android 10
pm uninstall --user 0 com.samsung.android.stickercenter # android 10
pm uninstall --user 0 com.samsung.android.calendar # android 10
pm uninstall --user 0 com.samsung.android.messaging # android 10
pm uninstall --user 0 com.samsung.android.rubin.app # android 10
# ant radio
pm uninstall --user 0 com.dsi.ant.service.socket
pm uninstall --user 0 com.dsi.ant.sample.acquirechannels
pm uninstall --user 0 com.dsi.ant.server
pm uninstall --user 0 com.dsi.ant.plugins.antplus
# gear vr
pm uninstall --user 0 com.samsung.android.hmt.vrsvc
pm disable-user --user 0 com.samsung.android.messaging