Basically, currently both services have their pros and cons.
I like the PSN store and its game content better (Super Stardust HD IMO is the best effort of the games not being distributed on disc as well), I love the dedicated lag free servers for many games and best of all you can play online free of charge. The Singstore is also very cool:
http://uk.youtube.com/watch?v=y5YScW9V460
I hope a future music (-video) and movie downloads service will be similar on the PS3.
For developers the PSN provides far more flexibility, however integrating Microsoft's pre-baked Live functionality is easier.
Live advantages like in-game messaging, achievements (and OS features like custom sound tracks) should be dealt with soon by confirmed firmware updates. For example [edit]background downloading[/edit] support was also included through 360 firmware updates.
IMO achievements and custom sound tracks have been a bit overhyped. For many games sporting dynamic music like Uncharted: Drake's Fortune it does not make sense at all. For other games like Super Stardust HD the feature was added by the developers themselves, although nice for this sort of game I haven't used it at all. If it was important to me, I would have turned down the in-game music volume and use my audio system.
Gamerscore is IMO boring as it has little to do with actual skill, I am more an advocate of highscore rankings and potentially trophies for finishing games in various difficulty levels. A trophy room can be cool, but I am not really anticipating this much.
Home as a whole is IMO the most interesting and promising new development, which should greatly expand the social aspect of the PS3. This I highly anticipate!
IMO don't expect too many 360 firmware advancements, its 16 MB firmware flash memory is full, the PS3 has two 128 MB firmware flash memory chips which are largely empthy, Sony was planning ahead.
PSP remote play and connectivity also seems cool, but I don't have a PSP (yet) to try this.
