Mines is just a pain to deal with in 10s for various obvious reasons (not having nearly the same amount of CCs/AoEs/Grips etc, not to mention you don't have enough people with engineer belt tinket to trivialize it in some cases). Missile is honestly very easy to deal with unless you get two non-empowered ones in a row, then you risk overlapping between the previous one ending and the new one starting which can lead to some chaotic situations. Mines also needlessly extent the fight in 10 man by a good margin. If you have people who can consistently dodge missiles (especially during magnet/empowered lasers) it's the easiest way to go. Killing missiles does take the "skill" component out but I feel adds a very hefty check in regards to having the right comp to deal with it (both dps and CC wise).
I kinda understand why 25 mans kill mines instead but honestly if 10 mans can deal with missiles, I don't see why 25 mans can't either. More people, more chances someone will screw up?
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Also, are people really sure the empowers aren't just predetermined from the onset, and if you kill an empowered weapon the next one in line gets it or something? The reason I'm wondering is cause we tried this order once in our 10 man -
1: Empowered Missile + Laser (kill Mine)
2: Empowered Laser + Missile (kill Mine)
3: Empowered Magnet + Laser (kill Missile)
4: Empowered Missile + Laser (kill Mine)
5: Empowered Magnet + Missile (kill Mine)
6: Empowered Mine + Laser (kill Mine)
7: Empowered Missile + Mine (kill Laser)
The bolded part is what our assumption was - that because we had just gotten empowered mines on the 6th wave, we would not get them again on 7. However, he empowered mines at that point again and it was regular missiles. Since then we have just killed mines on every wave and only have to deal with them once after the 6th belt.