Obviously software was totally different back then, and Apollo 11 was much more than a software project, but FWIW the Apollo guidance computer software was 130416 lines of assembly[1][2], while Facebook is probably at least 100 million lines of code at this point[3]. Also note that Facebook uses languages that are much more expressive than assembly, so "1000x as much code" probably indicates much more than 1000x as much logic being expressed. The reason Facebook and Gmail seem relatively simple is because they're designed to feel simple so they can be used by regular people, but the full implementation details are very, very complex.
while Facebook is probably at least 100 million lines of code at this point
...which, if I were to guess, consists of a significant amount of "do nothing" or otherwise useless abstractions that either were put there dogmatically or once served a purpose but no longer does. This is reasonably prevalent in Enterprise software but I imagine the much higher churn in Facebook code also increases the amount of cruft that gets thrown in or otherwise left behind.
Search HN or the Internet in general for mentions of Facebook's app being bloated and you'll find that even non-technical users are at least somewhat surprised by this gross inefficiency.
[1] https://qz.com/726338/the-code-that-took-america-to-the-moon...
[2] https://github.com/chrislgarry/Apollo-11
[3] https://www.quora.com/How-many-lines-of-code-is-Facebook