I suspect this has to do with the lack of video. I could be wrong of course.
Lemmy
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This would be the biggest part. Right now Lemmy cannot be compared 1:1 but somehow I don't really miss video content.
Also reddit has a lot of ads and some of them are video ads which consume data just for displaying them.
I dont miss the amount of unnecessary videos. So many of them could have just been text that could be read before the video could even load.
Part of this may just be that Lemmy does not stream video through the app right? Also most Lemmy servers force very small image sizes.
Maybe you should switch from the Reddit app to using Firefox. Reddit's app is very data hungry
/r/place was super bandwidth intensive. They managed to turn each individual pixel change into several KB of data.
I didn't even place or follow r/place changes. Just go on there, look at memes and how the map has evolved since.
But still just moving around is very bandwidth intensive.
Not necessarily the best comparison if it's just aggressively caching. The real comparison to make is analytics tracking events and other evil things like random battery hungry background tasks