Is cross-platform (not cross-generation) play possible in Destiny?

I know that cross-generation (PS3 player with a PS4 player) is not supported but can a XBOX One player play together with a PS4 player?

Solution 1:

As far as I know, no it is not cross platform. Bungie stated it is due to 'fairness' as the consoles (/ pc if they added it) would all be slightly different in performances.

Bungie Explains Why Destiny Cross-Platform Play Isn’t Happening

Destiny won’t feature any sort of cross-platform play [...] This isn’t due to a technical issue though, but rather Bungie not wanting to give players on the new consoles an unfair advantage, as Bungie Engineer Roger Wolfson told Digital Trends:

I’ll speak for the hypothetical player. I have a disadvantage sniping across the map because [my opponent with a new-gen console] is only two pixels on my screen and I’m four pixels on his. You see that in the world of PC gaming, where people are always racing to the best video card to give themselves the advantage.

Regardless of where the reality is, there’s definitely a perception among gamers that better hardware means you have an advantage. We don’t want to have to enter that fray, so to create the best, most level playing field, both actually and perceptually, we separated it by platform.

The above is the reason given in the linked interview, by a Bungie engineer - though there are as stated in the below comments other reasons for why it is hard to cross platform a game in general. For example SONY and Microsofts platform policies / ability to work together.

Solution 2:

No, this is not possible, unfortunately. See this post for an earlier similar question. Here I explain that the servers are seperater for each console, but you can transfer your profile cross generation, but not cross system (Ex. from PS3 to PS4, but not PS3 to Xbox 360/One).