This sounds great when you envision that big company as Amazon, Google, Microsoft or Facebook. It sounds less so when you envision that company as Oracle, eBay, Yahoo! or SAP. Some large companies are mostly going to teach you politics, byzantine process and spending money as a means of scaling bad software.

It's important to differentiate skills learned at big companies. Some are very useful, but others are coping mechanisms that have no place in a startup. Meanwhile, the scrappiness and well-rounded skill set learned at a startup will almost always have a place in larger businesses.

My own personal recommendation for early career workers would be to prefer the cream-of-the-crop mid and large companies where you'll get useful experience you can't find anywhere else, then prefer startups and leave the slower-moving and more dysfunctional larger companies as a last resort.