I came to AT&T after having worked at a couple small companies (I'm retired now as of last Winter.) I agree with the poster who said the grass is not greener there. There are pluses and minuses with either one. On the small company side, I had no pension and the 401k in one case had zero employer contribution and a very tiny one in the other case.
Company politics were AWFUL in both places. One was a family owned business and you had to be VERY careful to never offend ANY of the owners. The other was not family owned, but the owners/long time employees were a closed clique. At either place, if anything went south - and things did at both places - if you were not part of the family or the "in" group, you could easily find yourself thrown under the bus.
Pay raises were tiny and infrequent. One woman at the first company I worked at had not had a raise in 10 years because the owner (a millionaire several times over) decided he was paying her "all she's worth to the company."
No union at either place, so you are 100% at the mercy of "the boss." Your job was subject to being ended or changed on a whim, as was your salary, hours, vacation time, benefits, etc.
The second small company I worked for went bankrupt and folded rather suddenly. They'd lied to us for months about how we were doing and suddenly in a matter of less than six months, about 240 of 250 employess had no jobs. The others went to work for the sweatshop that picked up the pieces of what was left of the company.
Now there WERE good things as well - You got to interact with management all the way to the top, so they knew who you were and what you were contributing. When things were going well, that was usually a good thing. It felt less impersonal than a big corporation like AT&T, but you also knew you were never likely to be part of the inner circle unless you were making them REALLY big money.
On the whole, I ended up with a MUCH better retirement from working at AT&T (although I sweated out YEARS of surpluses) than I ever would have had working for the smaller companies. That's something to look at depending on your age and how far from retiring you are.
So as has been pointed out, there are good and bad points on both sides. Just don't be looking for nirvana if you make the jump. It might work out very well for you, but small company does not automatically translate into better place to work.