If you thought it's the same whether you post photos on Instagram or Facebook, then you're wrong. In fact, photos posted on Instagram receives more interaction than photos posted on Facebook directly.
SEO guru Neil Patel has shared a case study(see point no. 7) recently showing data that photos being posted on Instagram (which is automatically shared to your connected Facebook account) received 23% more interaction than photos natively shared on Facebook.
So, why does this happen? Well, there really is no explanation so far. Instagram is owned by Facebook; therefore, one can assume that both platforms would receive equal priority on Facebook.
To test the theory, I actually tried it on my own profile. And the results were astonishing. Photos I've posted on Facebook through Instagram received more reach than other photos uploaded directly.
So, the posts that you are sharing on Facebook through Instagram does not only have the simple difference of a "via Instagram" tagline on it. It actually makes quite a difference in terms of outreach.
And this is why it's better to post your photos on Facebook through Instagram instead of a native upload; that is, if you're concerned about more people seeing and liking your photo.
In case you don't use Instagram already, I really suggest you do.