Jobs at big companies are less stable and end with less notice than at small ones, at least in my experience. In a small company, particularly one with engaged and transparent leadership, everyone knows what’s working and what isn’t and about how long the latter can be endured. At a large company the vast majority of jobs are susceptible to the whims and whispers of a few (who likely aren’t engaged and feel they can’t be transparent).

Obviously this is just one person’s opinion.