I owned an EMC-20H that was trimix enabled and I am not sure how the profiles or features may differ from the EMC-16, but here's my thoughts based on my experience with the EMC-20H and the Predator.
The Cochran set on "0" conservatism gets out of the water faster than anything else on the planet. That was nice for offshore diving with the EMC-20H as a back up and the primary deco information coming from custom cut tables and a slate. It gave you something to go on if you got badly off plan, and it gave you a minimum time to surface profile in the event of an emergency, bad weather moving in, etc.
Cochran reps I talked to agreed it was too liberal and privately suggested never diving it as a primary deco source at less than 30% conservatism. In practice, I found I needed 40%-60% conservatism to ball park match other trimix computers.
The EMC-20H did automatic gas switching. You could delay that by setting maximum depths and minimum run times required before gas switching was enabled. it worked well enough on OW dives, but for cave diving I needed a lap top and some very precise planning to prevent it from switching to 02 during a shallow part of the dive, then "killing" me after i went below 20' following the cave profile deeper on the way out before again shallowing to 20' for the deco stop on O2. I lost track of how many times that POS decided I was dead thinking I was on 02... The major downfall of the EMC-20H as a tech computer was the automatic gas switching and the idea that it "told" the diver what he or she was or should be doing and then assumed that was the case.
-----
With the Predator and Petrel, Shearwater uses a totally different philosophy than Cochran where the computer just gives you advice, then lets you decide what you really want to do and you can not only start and stop programmed gasses at your preference, but even change the gasses is uses underwater after the dive has begun. Handy in lost gas scenarios and or if you bail out to back up gasses or someone else's reserve gas (unlikely, but the computer can accommodate it).
-----
With that in mind, if you are OW diving, I'd rely on the Predator and use the EMC-16 on zero conservatism and slowly increase it until it starts to give run times similar to (but still slightly less than) your Petrel. If you are cave diving I'd leave the Cochran home and use it as a paperweight.
