The thing is that big companies rarely provide as much job security as they seem to at the time you take your offer. Ask the folks who joined AT&T in the 1950s, or Digital in the 1970s, or Sun or SGI in the 1990s, how it worked out for them. When you're at a big company, you're often at the mercy of market forces and executive decisions that you can't see. In a small company, all of these are at least visible to you.
I'm not entirely sure that I'd agree that you learn less at a big company than a startup, though. I learned a lot more in my first year and a half at Google than I did in my 1-2 years at each of the two startups I'd worked at previously. It does level out after your first 2 years, but that's the time to practice soft skills like leadership, mentorship, influence, estimation, decision-making, and so on as you gain trust and get put into positions that don't exist in a startup.
I can’t speak to AT&T, but my friends who joined Digital, Sun and SGI in their twilight years got to work on fascinating engineering challenges and built up great professional networks. When those companies wound down, some took buyouts with several job offers already lined up for them. In many cases, entire teams were hired intact by other large firms with generous retention packages.
There’s nothing wrong with startups, but there’s nothing wrong with going to the giants that are doing Real Engineering, either. Both can lead to great careers.
I'm not entirely sure that I'd agree that you learn less at a big company than a startup, though. I learned a lot more in my first year and a half at Google than I did in my 1-2 years at each of the two startups I'd worked at previously. It does level out after your first 2 years, but that's the time to practice soft skills like leadership, mentorship, influence, estimation, decision-making, and so on as you gain trust and get put into positions that don't exist in a startup.