AMD APU + GPU crossfire VS Discrete Graphics Card

My sister wants me to build her a PC for college but she would also like it to run some basic games and her budget is $500. I am trying to decide if it would be more cost effective to go with AMD APU + GPU crossfire or a Discrete Graphics Card. After doing some research I can't find many benchmark's comparing these two options. 

I have put together 2 builds

AMD APU + GPU Crossfire

&

Discrete Graphics Card

Both builds are a little over her budget so I will just throw in a few bucks to cover the rest. If you were doing this which build, or variation of one of my builds would you pick? 

 
 

examples of some games she's playing? i was able to play return to castle wolfenstien on my AMD A10-7800 no problem for example. 


 

The discrete GPU is by far the better option, especially since APU + GPU setups (when using hybrid crossfirex, not when using the APU as a CPU and the dedicated GPU as the only GPU) can have some nasty stuttering problems. Also, I'd suggest getting an R7 265 or R9 270 instead of the 750 Ti as they are more powerful cards. If heat/power consumption are a problem then of course the 750 Ti is better. Also, as anarekist suggested, depending on the games she plays she might be find with just an APU.

At any rate, if solely an APU is not sufficient, I would probably get this build: http://pcpartpicker.com/p/YXFjBm

That MSI board is capable of overclocking; tom's hardware just posted an article where they used it to overclock the Pentium G3258 to 4.4 Ghz. http://www.tomshardware.com/reviews/pentium-g3258-b81-cheap-overclocking,3888.html

Well, I gave her my old 360 console and games when I switched to PC but that console fried a couple months ago. So she was playing FPS and racing games but im not sure what she will play when she starts putting together her own collection. I think she will be playing whatever cheap games I can find for her at first but would like it to handle some newer titles on low settings so the system will last her a while without upgrades. 

 

Well the G3258 + R9 270 should be able to handle most games on medium or high settings.

Seeing as the Pentium is only a dual core I suppose it might be beneficial to pick up a good Z97 board so you could throw in a broadwell quadcore if she needs more CPU horsepower. But I would expect an R9 270 to be able to handle everything she wants and more, although not at max settings. Assuming a 1080p resolution.

Yes she will be using a 1080p display. Thanks for the advice I think I will go with the G3258 + R9 270 and look at some Z97 boards.