Your system will be just fine. You have more than enough RAM and your CPU is still a fine gamer. For the resolution you are playing at your rig is more than enough
I work for EA. I talked to Bio's development team, with some new tweaks etc for max settings 560/6950 or above is needed to play with no framerate drops etc, yes you can use max settings with a lesser card but don't expect 60fps on them.
One thing to remember when playing games and if a video card will be able to handle it is what your screen resolution is. Your screen resolution is on the lower end so a graphic card like a GTX580 would be overkill. The higher the resolution you have the better video card you need.
I play at 1920x1080 with a GTX480 and I have no problem playing any games at high settings at this time.
Here is a good site that gives you excellent bench scores with different games at different resolutions on all the video cards out there
That's also an excellent site to get good reviews and they have excellent forums for getting help.