I built an i3 2100 system for someone earlier with the integrated graphics, so the power consumption was minuscule.
Initially I used the Corsair CX430 unit, which did not work properly, the computer would not shut down.
It would restart approx. 2 seconds after powering off. So thinking the unit was faulty, I sent it back and got a brand new replacement.
It did the same thing again with the replacement unit, so I decided to add a graphics card to the system and try to shut it down then. It shut down fine since the power consumption of the system was increased...
So I believed that the PSU would not shut down properly when the system wasn't pulling enough power out of it.
Ended up getting an Antec 400W PSU which was at the same price. Shut down no problem. The person I built the computer for ended up getting their system about 3 weeks later than expected :s
So I personally would stay away from the Corsair CX PSUs if using a low-wattage system.
I found this thread which indicates that there was a problem with the original CX series when under very low loads
Couldn't find anything with the CXv2/v3 series so the problem has probably been fixed.
You have to remember that these are budget units, so the quality is not as high as expensive units, so it is more likely that there will issues with the power supply.
Solid 400W options are Corsair CX v2/v3, Strider Essential, Antec Neo Eco.
Aywun Mega Power Pro is the same platform as OCZ ZS if I remember correctly, so will be solid.
Also I found a review on the Aywun Megapower Elite, which reveals that it is the same platform as the Silverstone Essential, so should be decent for a budget build.