The higher the impedance (ohms) the more power you need to drive them.
Meaning if you got the 600 Ohm version you'd need a proper amp to power them properly (despite the STX saying it can drive them up to 600ohms)
The 80 or the 250 will work fine on the STX, but most say the bass on the 80s is a little better.
The difference is the amount of background noise/static you can hear. The DAC in the STX converts the digital signals to analogue and so creates static in the background. On headphones with for example 5Ohm impedance, you'd hear most of it. Then the higher you go up, the less background noise can make it through to the headphones...so in theory, the 250s should give cleaner sound than the 80s, although, I use the 80s and it eliminates pretty much everything tbh.
The disadvantage to getting higher ones is the fact you need more power to power them. For example, if I put my 80s straight into my iPod, they do still work to reasonable noise levels. I'd hate to hear what happened to 250s though, as they'd just be too quiet to really use.
If you aren't getting the STX straight away and so you were running without a headphone amp, then you need to get the 80s really. Although, I don't really see that as a con because according to reviews online as I've said, most people rate the 80s more highly anyway.