For Eliminator Spec:
1. PVP = Eliminator. Because "Increases the critical chance of RAIL SHOT [...] by 15%."
2. PVE = Eliminator. Because " Increases the critical chance of Power Shot and TRACER MISSILE [...] by 15%".
With Arsenal spec you should use Rail Shot and Heatseeker Missiles when the heat signatures (Tracer Lock) are fully stacked (after 3 Tacer Missiles).
For Pyrotech Spec:
1. PVE = Combat Tech. Because "Increases the damage of RAIL SHOT [...] by 8%."
2. PvP = Eliminator. Because "Increases the critical chance of RAIL SHOT [...] by 15%."
Remember, as a Pyrotech u should use Rail Shot on every cooldown. (Prototype Particle Accelerator + Superheated Rail + Rain of Fire + Firebug).