The biggest thing for me is remove the red tape and bureaucracy. This is the worst thing big companies do. Every time they see a problem, they think the solution is another checklist. Someone needs to make CTOs understand that if the programmer has to fill out six checklists, he's not actually being more careful. He's most likely being LESS careful, spending time checking off boxes instead of actually testing stuff.
One idea that I think might work for a big company to appeal to startup-minded people is if it were actually organized like it had a bunch of start ups. Make teams of people that are geared towards actually being able to create a product, but don't put a pointy-haired manager over each one who report to directors who report to VPs. Give them the autonomy to finish products the way a start up would, working with their business customers the way a start up learns from its users. Rather than promotions and titles, pay them according to the worth of the products they develop. If the business customer justifies a project saying it'll add 10 million yearly revenue, maybe the team should get 1 million split evenly between them. If two people can pull off such a product, they're worth more than the team that needs 5 people to do it. I'm sure there are things that still need to be considered with this idea, but I think it has some sound principles. In theory I think I'd prefer working at a place like I've described versus the traditional org chart.