Are they? Why would they be?

There's not a whole lot of reason to suspect that the networking models differ significantly. Although Destiny has a massive development team, you really don't want to do things differently on different platforms if you can reasonably avoid it. They certainly seem to have built the foundations of their graphical systems like that, at least; according to their SIGGRAPH presentation, the exact same 96 bit-per-pixel G-buffer format is used on all platforms, and that layout was heavily influenced by the seventh-gen console's capabilities.

Bungie is going to take advantage of the new platforms when it's easy to do so, but Destiny on PS4/XB1 is not designed exactly how it would be if it were strictly an eighth-gen game. Not that doing so would necessarily change the networking anyway, it's not like the internet itself changed into something totally different overnight.

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If the underlying game behaves deterministically equivalently on the differing machines, then there shouldn't be any large barrier to synchronous networking a la Halo's coop.

If it doesn't, but is still almost identical, asynchronous models like what's used in Halo's multiplayer might still work.

Because the network protocols are still the exact same?

Are they? Why would they be?

Because the internet. It's universality and interoperability is it's key strength.

The whole point of a new console is to improve, grow, move forward. I don't understand the assumption that both generations are using new base-level programming architecture but the brand new system is using networking methods that could be ten years old already.

Actually X86-64 has been around for over a decade. It's a 64 bit extension of x86 - which itself has been the dominant processor architecture in desktops for 30 years. The last gen of consoles used different ones because they were simpler and cheaper at the time. Now the trade-offs have changed and both Sony and MS just stuck with X86-64.

AFAIK, the most recent change to internet protocols has been the SLOOOW introduction of IPv6. Getting any further improvements over raw bit-rate increases would require the collaboration of a huge number of entities across literally the entire globe, would take years and billions of dollars. Not even MS has the clout to drive that through on their own.

Multiplayer online action games generally use the 'UDP' protocol - it's simple, quick, and fire-and-forget. Any further complications reduce performance and lessen the impression of it being real-time interaction.

My whole point is not to say it's impossible, but that it's careless to say "cross-generation play faces no technological hurdles or barriers." I'm sure if it was as easy as that, we would have seen it before.

Before, the leaps between console generations were much more significant at a base level of capability and cross-gen games didn't exist much. Now, the differences in capability is much less fundamental and Bungie themselves said they want you to have the full Destiny experience whatever generation you're playing on.