Well you're right in that PS3 started to outsell the Xbox 360 towards the end of its life cycle but one could argue that the reason for that is because everyone already had a 360. Did they ever surpass the 360 in total sales? I'm not sure they did. I've seen that 3:1 ratio also but I think that's solely between the Xbox One and PS4.
Regardless, you asked how more people can be on Xbox Live than the PlayStation Network if this were the case. The answer is simple: online subscriptions =/= consoles sold. You don't have to get an online subscription in order to play the system.
People say that competition is better on Xbox Live for PvP play (maybe not necessarily for Destiny) and maybe it is. However, IMO, that's only because the pool of players is much larger. It's always been that way and despite console sales, I don't see it changing anytime soon. Someone said earlier that people only get an Xbox because their friends have one but either that be proving the point that more people are on Xbox Live?
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Acording to the data i just read Sony sold 80 million PS3 consoles by Augest 2013, while Xbox 360 sold 78.2 million consoles by Augest 2013. This was from an article on geekwire, which was the first search result Google gave me. http://www.geekwire.com/2013/xbox-360-wii-ps3-won-console-generation/ Another article from Jan 2013 say at that time PS3 sold 77 million while Xbox 360 sold 76 million http://www.gamesindustry.biz/articles/2013-01-09-idc-game-consoles-discs-to-remain-revenue-mainstays-for-years-to-come Now I don'rt know how valid these articles and their numbers are but from where they get the information they report, they seem like a legitimate source.