Better in the respect that the PC PSU will likely have a lot less ripple and be massively more efficient provided you have some decent load going through it. From the datasheet the LM2596 has an efficiency of around 72%, this would go on top of your PC PSU's efficiency at whatever load you have on it.
One possible benefit you might see on 5.12v vs 5.00v would be if you are using the Arduino's analogue outputs to measure something and you need the accuracy to be super high, otherwise who cares about 0.1v.
What sort of load on the 12v and 5v are you planning anyway?
If I needed 5v or 12v near my PC and it wasn't an audio circuit, then I would use my PC power supply. PC SMPS are fantastic compared with a crappy LM2596 circuit from China.
Ahh right, makes sense
It won't be involving any audio so that's good
To answer your question, there isn't going to be much load at all really, will that be a problem?
There will be 2 - 4 (probably just 2 though) 120mm case fans and the arduino
Case fans will be on the 12v and Arduino on the 5v
If the (lack of) load will be a problem (I'll wait for your answer on this please), would I be best off splicing into just one of the 12v cables and adding a resistor in between it and ground. And the same for 5v? Would you be able to suggest a resistor please if that's necessary?
Thanks!