I've worked at startups and and big services companies. At startups, we've gone out of business in the middle of projects, or decided "we don't do that anymore" while we're doing it, and abandoned clients. As the lead of a small provider, I'm always a few screwups away from not being able to make payroll and losing all my staff, and if I'm hit by a bus or have a personal emergency, there is no backup.
At a big company, we had actual continuity plans, a diverse business that was not going to unravel over some minor thing, and thousands of employees that would be able to fill in if needed.
There are lots of exciting reasons to work with startups, or small providers, but there is a reason whi big companies exist and can charge a premium that covers their higher overhead