I guess the goal should not be to 'not fear' but to win over the competition by not allowing fear of the bigger size of the competitor.

There can be two pronged strategy-

* how is my small size an advantage - how can I maximise that advantage? Can i move fast, can i create specialised features which bigger competitor can not focus on and can those specialised features be of high margin? ex- Mac versus Windows in early 2000. https://news.ycombinator.com/item?id=17695388

* what can the competitor not do, because of the big size? Is doing some of those things bringing me enough advantage to pursue them.

I do not compete with shark, but don't put us in the same tank

https://en.wikipedia.org/wiki/Competition