You're free to use the same Guardians across both generations, as long as it's within the same company (Microsoft / Sony).
If you finish a game your Xbox One version, it should only take a few seconds before you can login with your recent changes on your Xbox 360 version.

How does that figure?

The installed base of the 360 and PS3 combined right now is probably somewhere in the neighborhood of 200M.

Not quite 200M; late last year the 360 wasn't even to 80 million sell-throughs, the PS3 was pretty near, and these consoles have had reduced sales since XB1/PS4 launched.

Granted, but you can call it 150M easily and that's still almost ten times that of the next-gen consoles.

Game sales potential on PS360 is nowhere near what that number suggests, though. Some units no longer work, some people own multiples, some people have old hardware but no longer buy (or play) on it. The launch of the new generation has had a big impact here; PS4/XB1 versions appear to significantly discourage people from buying PS360 versions of cross-gen games.

It'd have to be a lot more than "nowhere near" to make the potential as low as that of the next-gen, though. You'd have to be talking about 2/3 to 3/4 of those units broken, dupes, or backups. Even if EVERY owner of a next gen console ALSO owns at least one last gen, that's still only a fraction of overlap. If every next gen owner owns a last gen console that is gathering dust, that still means that there are still another 130M last gen consoles out there. Let's say half of those are broken, or aren't seeing any new purchases-- fine, now it's 60M. That's still three times as many next gen consoles are out there!

The PS4 just hit 10M and is doing better than the Xbox One, at least worldwide if not also in the US at this point.

The PS4 is ahead even in the US. The front-loaded fanbase, and Microsoft's generally good holiday performance, allowed XB1 to slightly edge out PS4 last December. But the PS4 has sold more units every other month.

Sony continues to promote the game as if it was an exclusive, and Microsoft continues to let them do it.

Sony cut a marketing deal with Activision for Destiny. IIRC, it's the same reason (with Microsoft instead of Sony) that Call of Duty has at times seemed like an Xbox title.

The deal explains why Sony spends money advertising and promoting Destiny on Sony hardware.

It does not explain why Microsoft does not spend money advertising and promoting Destiny on MS hardware as they do for other third party titles that are not necessarily exclusives.

Usually there's at least a minimum of "me, too" marketing so that the audience knows a title is NOT an exclusive. Microsoft's silence about the title is deafening, and I think it's because it is a direct threat to the Halo franchise-- and quite predictably so!

This is why...

It'll be interesting to see if Bungie's 360-owning following gives the new title a boost on either of Microsoft's platforms or not.

...some people are predicting that Destiny will cause a large spike in PS4 sales, much moreso than other platforms.

It's definitely strange, though. Unless the attach rate on existing users is absurd, Destiny is going to have to sell large numbers of PS4s and XB1s.

Out of the three possibilities, it is far more likely that Destiny would sell far more on last gen than is expected, if not more than on next-gen, or would miss its high sales targets altogether. I think Destiny may move some 360 owners into the PS4 camp, but because there is a 360 release, they don't have to make that move now-- they can make it for the sequel, which is probably what I will end up doing.