According to benchmarks that I and others have been doing recently (not that Quadrant is the best damned benchmark there is, and it really does need some significant updates but that's another thread altogether), the GS4A is working precisely as it should be. With Antutu the results are somewhat stable (as of the 4.0.2 Antutu update from a day ago), and again it's providing results that are where they should be.
For Quadrant I'm getting 12,000+ scores now that Safestrap is detecting and initializing all for cores properly (whereas before it wasn't and the scores were in the 8,000 to 9,000 range), and with Antutu where I was getting scores in the 22,000 to 23,000 range they're now pushing almost 28,000 - yesterday I did a test after a reboot and got 27,958 which is my highest score to date.
(and realize these are "stock" speed results, we still don't have overclocking yet because of the locked bootloader and stock kernel on the I537 AT&T model which I and many others have hence the necessity of using Safestrap - thank you again, Hashcode).
So for me, I've yet to encounter issues with the GS4A I have, not one worth complaining about or even considering selling it. But then again I got mine for $100 on craigslist and I haven't been anything but loving it so far.
I use MX Player (which I finally bought a few days ago after using the free version for nearly 2 years now), plays everything I throw at it without skipping a beat (or a frame for that matter). You may be trying to play items that aren't being hardware accelerated properly on the GS4A - make sure you enable the HW+ decoder (in MX Player under Settings - Decoder) which is the best way to handle decoding content with that app.
As for the others, I can't say for sure. If you're running a pure stock ROM then perhaps running a custom one might alleviate some of the issues you're mentioning. It's entirely possible you could have a defective GS4A as well - but I've used a GS3 before and the first time I used a GS4A (even before owning one) I noticed a huge difference in performance even on the demo model I was testing out in an AT&T store: the GS4A just left the GS3 in the dust, basically (and the GS4A is built to work in dust, go figure...).
I don't know which specific GS4A you have (International I9295 or AT&T I537) so... check into the custom ROM thing - for the I9295 there are several available but for the I537 we're still stuck with just the AOSP ROM which can be installed using Safestrap. Hopefully designgears will have that "leak" of the latest build for our I537 model here shortly...