The amount of memory a graphics card has is not as important has the speed of the graphics processing unit(GPU). In this case the 5570 does have a faster gpu and will be able to produce more FPS and higher settings than the 4350. With many games the auto detect feature doesn't work very well, Usually I just set my stuff up manually and see how it runs and fine tune it from there. Even setting it to high settings manually the 5570 is only a mid-level gaming card, to run starcraft 2 on high I would recommend atleast a 5770 or the current best bang for the buck card the GTX 460. You may also be limited by the CPU, RTS games use alot of the cpu for the AI. Here's a Benchmark for starcraft 2 and many video cards the 5570 is the worst performer(it gets handily beat by cards that have less memory).
http://www.techspot.com/review/305-starcraft2-performance/page4.html