The Corsair AX1600i wins in 3 out of 9 comparable specs, with 4 ties. Its biggest advantage is Wattage (88% better).
Prime TX-850 wins in 2 specs (MSRP: 66% better).
Recommendation
Choose AX1600i if you want the best overall performance — especially wattage.
Choose Prime TX-850 if msrp matters more to you.