I have both a 03' CBR 600RR and a 04' R6 so here is my $.02:
I picked up the 600RR the end of last year to replace my dual purpose F4i track/street bike. First impression of the 600RR is that it's more geared towards track use, the seating position is more aggressive which can take a toll on long rides. The trunk space or now known as lack of trunk space is a big hit for a street riders. Something small but also important for magnetic tank bag users, the 600RR has a plastic tank cover, so don't think about using one of them. I used my 600RR as a daily commuter for about 1,000 mi I was pleased with how it ran I didn't get fatigued or have any issues on long rides. The lack of power below 8 Grand is a bit of an issue though for a daily commuter. Then I put the bike on the track and found out where it was intended to be used for. The bike would turn in much quicker then my F4i and if you keep it above 8 Grand the girl pulls really well. You can purchase a 600RR and put it on the track bone stock and click off some good times with it, but for a true junky fiberglass, clip ons, & rear sets are a plus.
I've since converted my 600RR to a track only bike because of this.
The R6 is a nice bike, seating position is about the same or a little better then the 600RR for street use. The seat is also more cushiony for those boney butt riders out there. The power band is smooth all the way through so it makes it great for the street. The trunk space is not as large as a GSXR but I can get a small can of Honda cleaner, tools, and a disc lock in the trunk with space to spare. There is an annoying vibration in both the clip ons and the pegs on a stock R6. To the point where my feet start to fall asleep on long rides, and I have to take my hands off to relax and shake them at any red lights. I've given my EX girlfriend a ride on the R6 and she complains that her knees hurt after riding on the R6, we found that the seat height and foot peg positions compared to the F4i is what is to blame. The oil filter is on the side of the bike which makes for really easy oil changes, no more getting oil on the header pipes.. Woo Hoo!! I haven't taken the R6 on the track so I can't compare it there, but talking with track riders they love the bike.
If you are looking for BLING I believe the 600RR gets more props because of the undertail exhaust. For a good all around street bike I would have to go with the R6 since the power band is better. Though it looses a bunch of points due to the vibrations in the pegs & grips. Either bike you go for you will not be disappointed.