Notnessary

Some big company already has several Labor certificates on hand. So, you can just use the substitute labor to apply the I140

For new labor, big company is not nessary fast than small company.
Labor approve or not depends on whether you can enough reason to approve that the company can not find any US work with proper salary for your position.

Some big company maybe has LOT OF people to that apply the job. Small company maybe has very small number of people who apply. So, never know.