For one, I don't believe a full version of Home will exist on either of these platforms.
PSP Home will most likely be a drill down version of the PS3 with possibility of accessing your Home apartment but no venture out into the lobbies. The ability to send text messages using a mobile phone to friends in Home and/or prehaps access to a 2D mobile website that lists your friends, purchases, and any events in Home. I highly doubt a trimmed down version of Home will be implemented on a mobile device. I hope Sony proves me wrong.