The PS3 uses an enhanced XMB interface that is better than the one on the PSP.
Now my PSP has better media functions than the 360 (apart fom the streaming).
The music player has more options, can deal with tags properly, album art etc.
The video player has more options, can deal with aspect ratios and other settings.
From what I have seen the PS3 improves on this.
What the 360 has at the moment is this MCE extender, which I don't think that many people use. At the very least you need windows media centre 2005 (not many computers came with this), or Vista Home Premium/Ultimate.
I am sure some people on these forums will disagree, but I don't think the media centre extender is something most people will know how to use or care about, especially when they realise they would have to convert their videos or do some transcoding (like a lot of people know what that is!!).
The PS3 doesn't have this streaming thing. They are going more down the location free player oute by storing the mdedia on the PS3 HD and then streaming it via your LAN or wifi or Internet to a PSP or other Sony Device with Location free capabilities. Again I don't think most people will know how to use this.
Most people will just play music or pictures or videos from a memory stick or Ipod or something like that. I think there is more features if you do this on PS3 at the moment. I don't think MS are concentrating as much on media player style functions as they are too busy selling video content in the USA, which gives them revenue, rather than developing better media player features that may stop people using Windows Media Player (imo).
All of these are just my opinion.
Ultimately the biggest problem on both machines is that the video needs to be a certain format. It all depends which websites start to release video in native formats for these devices. Many sites already offer video pre-formatted to ipod/psp formats. I don't know if the same sites are prevented from releasing them in 360/ps3 format at the moment, as this would conflict with the paid for content MS and Sony are pushing via there own online systems.
rp2000