Just a couple of counter-examples. Feel free to suggest more in the comments.
The notion that “film acting is small and theater acting is big” is a cliche. Great acting is bold and truthful, regardless of the medium. An underwhelming, trivial performance will vanish down the memory hole faster than you can say Amy Adams or Anne Hathaway. An overly “large performance” may live on in infamy, but if you regard “film acting is small” as a deep and powerful insight about acting, you may have a long career of cautious, eminently forgettable performances ahead of you. Sadly, many young people aspiring to be actors regard this kind of soundbyte-y, easily-graspable, facile pseudo-insight as exactly the kind of thing that will help them feel more comfortable walking into an audition.
Deep vs. shallow is a much more useful distinction than big vs. small. Have you studied a script carefully, thought long and hard about the situations of the characters and the worlds in which their stories play out? Their dreams for the future, and their fears? Their past setbacks and triumphs, particularly in the realm of forming and sustaining relationships? Have you considered corresponding relationships in your own life? Have you found a way to look at the scene as an opportunity to form or repair a significant connection, rather than a situation in which annoyance or injustice much be squelched? Have you found a way to light yourself on fire? If so, you will likely shine, in front of the camera or on stage, especially with the help of a discerning outside eye. If not, well, at least you won’t be too big. Never mind that in order to make sure you’re not too big, you’ll be watching yourself, monitoring yourself, measuring the “size” of your acting, cutting yourself down to size, where necessary. That might make you, I don’t know, a little self-conscious, but down’t worry about that. Whatever you do, don’t take a risk, don’t dare greatly, don’t expose anything raw. Because you know, if you do, they’re all gonna laugh at you. Just keep it small. Safe and small.
“There are no small parts. Only small actors.”