Level 3 is freaking huge. They have reserve bandwidth beyond your imagination, and they have some very smart people running it. Their infosec is literally military grade (They run milnet for the DoD IIRC).
Hacking Dyn is kid stuff in comparison. It happened to be a convenient single point of failure due to companies going cheap and outsourcing their DNS to save a few bucks and the bad guys exploited it. You can be sure that IT guys at the major sites are going to make darn sure it never happens again.
64.6.64.6 (Preferred--Verisign DNS)
8.8.4.4 (Secondary--Google Public DNS)