Graphics cards are getting smaller over each generation, as the die gets smaller as well the power need to run the card. However, aftermarket vendors usually make the PCB bigger and slap on a intense cooling system with some tweaks of their own. I personally would recommend a full-sized card, especially when you case is clearly designed for show and tell.
Would it make a difference? Only to the people who cared for small things. The R9 380 also is slightly more powerful than the GTX 970, and Mantle makes it all that much better in certain games. I hope that RAM was cheap, anything above 1600Mhz is not noticeable in the real world. I also wouldn't want anything above CL9. Not bad though, just hope you didn't pay a lot for it.
