Some of this is based on strong rumours, some is based on fact, it all ties together pretty well so i'm not going to seperate it all out.
Ok, firstly, some games on the PS3 already have friends invites, user hosted servers, clans etc etc. Basically GT5
s online mode is very much in its beta stages and is not an accurate representation of the PS3s online gaming. Warhawk and the Metal Gear Online beta were much better examples of what the PS3 can offer for online gaming at present.
Secondly, GT5
is going to recieve several updates over the next year, among these are additions to the soundtrack, visible and performance affecting car damage and an improved online system allowing invites and private servers.
Thirdly, while the PSN lacks features that the 360 offers, sony have promised that a firmware update (not Home) will bring the online experience 'up to standard' when compared to the 360. This indicates ingame chat, invites and an ingame XMB are a likely addition sometime this year.
Finally, Home: Home has been delayed and delayed, it is now slated for release at the end of this year. It has been developed more as an online community than an attempt at copying the 360 online (the aforementioned firmware update aims to do that). Older games WILL recieve updates and support for it, Warhawk, Drakes Fortune and GTA4 all had a mention that they will feature some form of unique content for Home (from what i've read, Warhawk will feature some kind of 'war room' where players can plan their tactics and uncharted has some form of side scrolling shooter minigame, no word of what treatment GTA4 will recieve but rockstar have promised 'something')
I can't provide a source for all of this mainly because i can't be bothered. It's mostly pieced together from official news, but other bits may be based on rumours.