IMO 6370 will not be able to provide a more fulfilling gaming experience. I would suggest you to consider a notebook with at least GT555 or HD 6770 for a 'reasonable' gaming experience on a notebook.
Notebookcheck comparison of:
Mobility Radeon HD 6370http://www.notebookcheck.net/AMD-Radeon-HD-6370M.40970.0.html
Mobility Radeon HD 6770http://www.notebookcheck.net/AMD-Radeon-HD-6770M.43955.0.html
I don't play BF2 as such but I like playing TF2 whenever I can, and on my current notebook (an HP DV6 6011TX with i7 & HD 6770) it gives pretty nice FPS. However, do keep in mind that such notebook's battery time isn't that good when playing games at High Performance settings.