The Core i3-3225 (Intel HD 4000) would consume less power when playing game, but when the system is idling, the A10-5800k will consume less power by about 7w.
Source:
http://www.xbitlabs.com/articles/graphics/display/amd-trinity-graphics_11.html#sect0
Looking at the power consumption while gaming, the A10-5800k consumes 41w more than the Core i3-3225 when using the Intel HD 4000. I really do not know how much power the Intel HD 4000 consumes when it is stressed. I would say about 12w - 15w is a reasonable assumption. So when playing games the Core i3-3220/3225 would consume 53w - 56w less than the A10-5800k taking the Intel HD 4000 out of the picture.
Okay so going with a Core i3 with a "disabled" HD 4000 graphic core means there's about 53w - 56w to play with to equal the power consumption of the A10-5800k. Before choosing a graphics card for the Core i3 system, let's just look at the performance of the A10-5800k's integrated Radeon HD 7660g. Benchmarks are in the following link to XBitlab's review:
http://www.xbitlabs.com/articles/graphics/display/amd-trinity-graphics_6.html#sect3
Basically the benchmarks shows that the integrated Radeon HD 7660g is slow than the Radeon HD 6570 discrete graphics card which really is not considered a graphics card for games. Therefore, you can simply buy a Radeon HD 6570 an install it into the Core i3 system and be done with it. The Radeon HD 6570 provides better performance and it only consumes about 25w - 30w of power so the Core i3 system will be both more powerful for games (but not by much) and also consume a little less power.
Alright, let's cut to the chase, you want better performance than the Radeon HD 7660g or HD 6570 can give you, but you also do not want to exceed the amount of power the A10-5800k consumes. You basically have two choice for the best performance. You can choose the Radeon HD 6670 which is relatively inexpensive (probably around $60 after rebate at newegg.com) and peak power consumption (meaning spikes up to) of 50w. The Radeon HD 6670 would slap both of the other Radeons silly. Your other option is the Radeon HD 7750 with a peak power consumption of 43w. It is basically the equivalent to the Radeon HD 6770 and it can be bought for about $90 after rebate at Newegg.com.
Power consumption:
http://www.techpowerup.com/reviews/ASUS/HD_7750/24.html
From a cost perspective, going with the A10-5800k would be cheaper than buying a Core i3-3220 + discrete graphics card. However, going with the Core i3-3220 + discrete graphic card will give you superior graphics performance (compared to the Radeon HD 7660g), and slightly less power consumption.