I own and have owned several GSXR's as well as my fazer thou, I own gixxer thou K7.
I had to have another this year. I owned a K3 750, and only sold it for the fazer so I could take the missus.
In my opinion the 750 is the best of the gixxers all round, great power and torque that you can use more of and better midrange than the 600.
Sometimes wish I had the 750 again than the gixxer thou as you can cane it more, but I use the mode switch on my thou and can cut the power if I wish.
Jumping from fazer to gixxer is very strange, but for general road riding the fazer is the best.
Don't even think of taking a passenger on a gixxer apart from frightening your pillion to death, it's pure agony for the rider!
Gixxers are great if you can keep your speed above average of 40 mph, as the weight kills the wrists. The seat is hard as nails too. The grin you get when you open the throttle and the soundtrack though is awesome, gixxers are very raw and scary fast.
I'd give one a go, but be honest with what riding you do most of.