We know that Sony uses
Prolexic as their third-party DDoS mitigation. We know how datacenters work, how distributed CDN (Content Delivery Networks) work, since they're basically half-standardized by now due to the time and investment required in building up to code datacenters to house this level of infrastructure. CDN and distributed infrastructure includes redundancy, up to a point depending on how much money Sony was willing to invest. Obviously we don't know how much they've invested into their infrastructure - some would argue not enough.
As for the rest, it's an educated guess on my part, which you're free to disagree with. I'm not going to claim to be an expert, but I think I have a decent understanding of how these things are set up, and you can find plenty of information on the Internet about these kinds of infrastructures.
As for this dumb PSN vs Live debate that's now kicked in:
Stevan Vidich, director of Windows Azure marketing: “Just about everything in Windows Azure is custom built and proprietary, including protection against DDOS attacks. We use standard DDOS mitigation techniques, but we also have dedicated third-party DDOS systems in place. Windows Azure also monitors for internally-initiated DDOS attacks and will remove offending VMs.”
Microsoft offers enterprise-level hosting solutions (think Amazon's AWS) as a product - they are in the business of having a stable, high-uptime system because it has to be appealing to prospective customers. They have experience in managing the kind of infrastructure Xbox Live is, and have had many years to get better at it since the Xbox 1, transitioning to Xbox 360, and now Xbox One.
Sony is not in the business of enterprise-level hosting solutions, and have a bad track record when it comes to online infrastructure. The original PSN hack, being a good indicator of the swiss-cheese that PSN was, and in some respects, might still be. Sony needs to spend more money on their infrastructure, especially since they have to cover such a wide area with it. I wouldn't say they're terrible at it, and that PSN is the worst ever, but it's obvious Sony is punching above their weight class in this one specific area. Sony is a multidisciplinary corporation with its fingers in a redonk amount of pies. And this is one of the side-effects: taking longer to recover from a DDoS of this size.
An alternate theory might be: they're taking longer to come back up, because they're checking for intrusions that might have happened during the DDoS. They have every reason to worry, in light of the recent Sony Pictures intrusion.
This isn't just XBL vs PSN lololo who wins. This is a big, complex issue, and it doesn't help to reduce the conversation to silly console wars.