I have a few friends who recently graduated bootcamps and inquired about how the size of a company impacts their day to day. As someone who only recently made the jump to a large company after many startups, I thought I had some things to chime in.
There's a few good articles on this already, such as https://danluu.com/startup-tradeoffs/, so I'll just speak anecdotally.
At a startup, you tend to be able to work on whatever you want, and have the opportunity to wear more hats. Note that this is note true at all startups.
On the flip-side, there's a tendency at larger companies for employees to develop a specialization. Typically you're working on a very specific team, but may feel pigeon-holed at certain points. There might also be points where you feel like a cog in a machine.
At startups, the tendency is more greenfield new feature work. At a big company, the work centers more around maintenance and building upon that which already exists. Either could be preferable depending on how rigid or fluid you like your solutions.
Expect to work longer hours at a startup. Expect to work shorter ones at a larger company.
Startups are the higher risk-- the business can disappear overnight, through no fault of the employees. At the same time, if you're one of the first hundred or so employees, you may do very well in the event of an exit.
Large companies are lower risk, but as a result, you won't be compensated as well as a unicorn startup exit (but still significantly more than a startup failure).
This varies-- the biggest thing to note is that talented people and engineers exist in companies of all sizes.
There is a tendency for people at startups to be more mission-driven. Most folks get into the startup game, if not for the lottery ticket, to make a large dent either at the company or in the industry.
This tends to be less so for tech giants. At a large company, due to pure numbers, you're more likely to find similar-minded people. But you might also find more bureaucracy and layers of approval. There are also more teams to pick from.
Large company wins here.
The best thing to do is to try getting experience at both kinds throughout your career, and see which you prefer.