That comparison is pretty meaningless without proper context — and actually rather deliberately misleading.
From the information I managed to gather it appears 2009’s picture was taken around 11.30am and 2017’s around 11am, a full hour before the start of the event. Also, the weather was quite different on those two days (2009 was a bit colder but dry, 2017 had warmer temperatures but some rain).
CNN’s gigapixel photo provides a more accurate impression of how populated the square was during the event.
Explore a massive photo taken during Donald Trump's inauguration speech.edition.cnn.com
Given the historic context (first president of colour) and the positive and negative media reports about Obama and Trump respectively in the time ahead, one can probably still safely assume there were overall fewer people at Trump’s inauguration than at Obama’s. But apart from the historic significance in 2009 (2013 had a lot fewer people) there could have been also other elements at play — such as aforementioned weather for example.
My main issue with this comparison is its blatant lack of objectivity and deliberate attempt to compare apples and oranges. Everybody (media and the crowds sharing it) is claiming the truth for themselves and yet when one then dives into those arguments one comes to realise how biased and false such reports actually are.
How should we be able to trust the media (or people blindly sharing such mainstream stories for that matter) if they obviously make up their “alternative facts” as they go, just to fit their narrative?
Trump’s infamous “you are fake news” sadly comes to mind here
The following article provides a pretty decent summary on that subject, including more details on estimated numbers of attendees etc.