graphics memory means next to nothing in judging a cards overall performance. it seems allot of people still think graphics cards are a stick of ram solely for graphics which they are not, allot of different things goes into a graphics card to determine how good it will perform. some of the slowest cards on the market are 1gb and some of fastest cards on the market are 1gb.
how you determine the graphics cards performance easily aside from reading some benchmark reviews is the model number.
in terms of radeon cards it goes like this
xyz0
x the first number dictates a new generation of cards but doesnt neccessarily mean they are faster ie the new 6 series are actually slower that the 5 series but they often come with updated features like 3d support, eyinfinity, new directx whatever.5 supports directx 11 anything above that atm is ok
y = the major performance number. this is the 1 you need t pay the most attention to as this number gets higher the speed of the card increases dramaticly the 4 is pretty slow the 7 or 8 are very fast. so yeah unfortunatly your 5470 isnt very good for gaming and is meant more for hd movie play back.
z= minor performance number - small boost in performance ie 5870 a bit better than a a 5850.
i cant find allot of info comparing the 8600mgt to the 5470 but what i came up with is the 5470 is a bit better but not by much you will maybe be able to play a few games your last laptop wouldnt run and some older games at a higher resolution (resolution being the only thing really that he gfx memory helps with)
hope that helps.