Next bike question - 600cc too much?

I'm looking at buying my second bike soon (once i relocate over-seas). Currently, the only bikes that i can afford without breaking the bank are SV650s and 600cc sports bikes. I'm not a major fan of the SV650s and have been leaning towards a GSXR-600.

I have had a 2012 Honda CBR 250r for the last year and a half, i ride it almost daily as a commuter but don't have the time for many "fun" rides. I have done maybe a dozen or two dozen rides in the twisties simply for the joy of it.

I can ride at the CBR250rs engines limit, however i still have "chicken strips", so i am not using the full potential of the tire. I've been told by some experienced, life-long riders that i need a bigger bike and that i corner well.

A GSXR-600 seems like it would be ok for a daily driver, great for fun rides, and fits within my budget. I'm just concerned it will hinder my ability to progress my riding skills!

So; is a 600cc a bad idea? will it hinder my progress?