I own both also (newer 360 w/ 60GB drive and launch model PS3 w/ 60GB drive and PS2 compatibility).
My quick summary.
The PS3's hardware is superior. The Blu-ray capabilities of the machine are fantastic. It's quiet. However, its software library and online experience is lacking. Most third-party titles are developed specifically for the 360. Therefore, the same title on the PS3 is not optimized specifically for the console (graphics don't take full advantage of hardware, bugs and glitches have been present in some titles). PSN is a mess and no where near as easy to use as XBOX Live. In-game XMB is limited. In-game messaging and music are both very limited. Trophy support is not available on all titles.
At least in the United States, the PlayStation Store has nowhere near the downloadable content available on XBOX Live. Additionally, there's very little original PS titles for download, and the selection of TV Shows and Movies are limited compared to Live. On this front, Sony also only lets you download TV Shows and Movies once (Live allows you to download your movies as many times as you want during the rental period, purchased content like TV Shows can always be redownloaded). There seems to be a movement on the PS Store for more original games (Pixel Junk Monsters, Eden, Fat Princess, Ecochrome, etc) compared to Live's vast selection of arcade and casual games (Contra, Geometry Wars, Uno, Prince of Persia, etc).
The 360's interface and media streaming capabilities are superior. It'll take whatever MPEG-4 based file you throw at it (.m4v or .mp4 doesn't matter). The PS3 is very picky with regards to MPEG-4. It doesn't support .m4v, and has limited support for .m4a (no album art, no meta data). The 360 can double as Windows Media Center extender. You can also schedule downloads via XBOX.com.
The PS3's interface is clean, but I personally don't like the computer folder/directory structure-like feel. Even though the PS3 is a DLNA device, I've had problems streaming to it (Sony has tried to fix these problems with recent firmware, but I still get drop-outs).
There have been several articles that have popped up on the development of the PS3. Apparently, Sony's hardware team developed the hardware and just handed it over to the software team, and you can really tell.
In a broader sense, I'm worried about Sony. There seems to be infighting going on between all three major PlayStation divisions (SCEA, SCEE and SCEJ) about what the PS3 is supposed to be. Personally, I would like SCEJ to leave the PS3's software interface and development to SCEE (they were responsible for the new PlayStation Store interface, which was based on the SingStar Store interface, and Home under Phil Harrison). I think SCEE has a broader vision for the PS3 as a online home entertainment/hardcore and casual game device (PlayTV, the new music video service, Home, Buzz, SingStar, Little Big Planet, etc) than SCEJ could ever understand.
I think the potential of the PS3 is much greater than the 360 in terms of the future. However, until Sony's Japanese execs let go of the notion of the PS3 as a "computer" and realize it's a "home entertainment device" it's going to remain in last place in at least the North American market. Possibly even the European and Australian markets (although it's currently in second place, I believe).
But that's just my opinion.