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I would say that the 6850 = a little faster than the 5850 so you might see a little more improvement.
iirc, the 5850 is faster than a 6850.
http://www.anandtech.com/bench/Product/512?vs=539
From their results, the 5850 almost always beats it.
The 6850 is only faster in Batman at 1920x1200 with Extreme Quality & 4xAA
so does that mean it would be worthwhile for me to upgrade to the 560ti or not?
IMO no. If I had to choose between the two I would go 560 Ti for sure, but for an upgrade I don't think its enough to warrant spending $100 bucks and changing out your system.
http://www.anandtech.com/bench/Product/539?vs=547
This is a comparison between the 5850 and the 560ti... looks like some minor fps gains in games granted will be a little larger gap since the 5830 < 5850
I personally feel you would be better off saving that 100$ and putting it to a better monitor or a higher gpu later down the road. Unless you can maybe put that 5830 in a media center or something were you are not loosing that cards functionality.