I know this is comparing apples and oranges, but that's what I've got: apples and oranges.
The Nokia 6600 has a 65,536 color 176 x 208 pixel display and a 640 x 480 pixel camera whereas the Sony SO505iS has a 262,144 color 240 x 320 display and a 1280 × 960 pixel camera. Both displays are bright, but the Sony display and camera win.
They're about the same size and weight, but the 6600 feels much more comfortable in my hand. Warm, round and buttons in the right place. The SO505iS is cold and a bit awkward (as if a digital camera and a phone got merged in the machine in "The Fly"). Having said that, the SO505iS is much better than the SO505i that it replaces. It's thinner and generally better designed. (The antenna doesn't stick out of your chin, the camera turns on when you open the camera cover, etc.)
The SO505iS runs J2ME and Flash applications whereas the 6600 runs J2ME and Symbian applications. The UI on the 6600 is utilitarian and simple whereas the Sony sports an animated background and a OS X sort of zooming icon wheel. The Sony has a two speaker stereo system and a stereo mini-plug for headphones where you can listen to music and watch videos from the proprietary memory stick in their proprietary media format. (You can record your favorite TV shows onto your memory stick and watch them on the train.)
The biggest difference is that you have to be a rocket scientist to figure out all of the message and data modes on the 6600. The blessing and the horror of the open system is that 6600 has to deal with all of the carrier inconsistencies and trying to figure out how to get online with the 6600 reminded me of just how screwed up the telco standardization process is. The SO505iS, on the other hand comes from the dictatorship of Docomo so what it lacks in flexibility and openness, it benefits in simplicity. Shoot a photo, click and send. Moblog away. I have yet to be able to send a picture via email from my 6600.
Both phones have lots of applications, but the Symbian applications are impressively Internet aware. There is an IRC client and IM client. Docomo, with it's rather closed architecture regarding networking has some cool applications, but they are really focused on providing content and services.
I would probably have a different opinion if I still used my Vaio, but the SO505iS really doesn't want to have anything to do with my Mac. The 6600 on the other hand, loves my Mac, talking to it in Bluetooth and even happily becoming a gprs modem for it. Zooming in a cab in San Francisco with my 6600 in my pocket and my PowerBook on my lap online was a great feeling. (Thanks for showing me how to do this Rael!)
Having said that, this is a totally useless review because you can't use the 6600 in Japan because we don't have a GSM network and you can't use the SO505iS anywhere outside of Japan because it uses Docomo's proprietary PDC network, or rather Docomo uses the SO505iS. Thus apples and oranges.