Pentium G620 would clearly outperform Athlon II 260. Combination of G620 & 6770 is far better than AMD A6. AMD A6-3650 would be ideal for casual gamers who don't want invest money on graphics card.
As you say that you have a decent ATI Mobility Card in your laptop. Find out the desktop equivalent of ATI 5450M.
Compare the desktop equivalent of your Laptop card with desktop
HD 6770 or 7750. Find the average increase in performance.
Then try to decide is it worth investing another 20K on desktop to get that much better gaming experience. The thing is if you are already having a laptop playing battlefield 3 decently at low settings, then is it worth getting a budget desktop which may not give huge boost in experience or atleast be a future proof config?
my suggestion: save some more money, wait for your laptop to get a bit older, untill it is struggling or unable to play the latest games you love, you will be frustrated with your laptop
. This will probably take a year. By then save up some 40 to 50K. you will be hungry to play the latest games
. Intel will release Haswell in 2013, which is Tock as Ivy bridge is tick. Tock is sure to give huge performance boost like Sandy bridge, Nehalem & Core. go for quad core Haswell & 7850/8850, that config will be rocking.