okay, so if you're not using a stand alone graphics card, don't even think twice before getting the A8, but if you're going to use a graphics card, then the i3 may be the one to go with. Unless you're planning to get something like a 7660D as a graphics card, in which case you'll be Crossfiring with the APU... In which case, the APU wins again. But if you're getting a graphics card besides the 76XX, then get the i3. If not, the A8 is good.
But, logically, if you're getting something to the level of an i3, I think you won't be going too much further than a 76XX graphics card anyway.
Intel rule for high end... But on a budget... Not so much.
$400 is my limit for the whole pc without an OS. Limited funds mean that I can either get an A8-5600k or an i3-3220 + HD5450.
The Intel HD 4000 is more powerful than the Radeon HD 5450. It is close to being as powerful as a Radeon HD 5550.
While the A8-5600k does not have the most powerful integrated Radeon HD graphics core; the Radeon HD 7560D should be a little more powerful than the Radeon HD 5550 / Intel HD 4000. AMD's APU benefits greatly from fast RAM. See link below.