The corsair 1333 MHz rams are capable enough to run at 1600 MHz speed. The default speed of AMD AM3 Ram support is 1333 MHz and even if you put a 1600 MHz ram in the AM3 motherboard, it will run at 1333 MHz speed unless some tweaking is done in BIOS. Perform the following steps and both of the Rams, 1600 and 1333 will run at 1600 MHz speed:-
1. Plug both the rams in your motherboard.
2. Turn on the system and go to the BIOS menu.
3. Now go to the advanced tweaking menu where overclocking settings are present.
4. You will find a setting called Ram multiplier with value as AUTO. Set it to MANUAL.
5. Now the setting for RAm multiplier, just below the previous setting will be editable.
6. Set it to X4, save the BIOS and restart.
7. When the system will reboot, use CPU-Z to get the RAm setting and you will find both are running at DDR3-800 setting.
Here you are running the 1333 MHz Ram at 1600 MHz speed but Corsair rams are known to work at that frequency without any issues. 6 GB Ram is enough for now. If you find any instability in your system then you can remove the 1333 MHz ram, but 1st try it out.
Doubt it..OP seems to be running corsair Value Select..i highly doubt that ram will pull 1600
maybe if fed some extra voltage...but more or less points towards system instability....
Most of the times windows may appear to be working fine, but you will face slow file copies/Bsods at unpredicatble times..
Also advise the member to put the memory latency settings at Auto/Default and not get carried away with the latecy timings of the 1600 Mhz sticks...already these are rated at cl 9 at 1333..not sure where they would end at 1600..probably on the darker side of 10...
Also , use a utility like aida64/volcano( i think thats the renamed version), and check the memory read/write benchmarks at both speeds
if the difference is small i`d advise letting them both operate at 1333