For dps sims will solve the dilemma. For healing and tanking it’s bit trickier.
I personally prefer “always on” power over procs which don’t necessarily occur when you actually need them. Therefore, hero ring with versa over cyrce for me.
The reason the ring is good is because if you run triple raw stat gems then the stats on the ring increase based on your mastery, which is increasing thanks to your ilvl.
Checking wowhead should give you a good indication of its power.
For Windwalkers for example, unless it gets nerfed it will remain one of the best rings available until S3. Simming yoursrlf should help determine if that is the case for you as well.
Seems I have been using the wrong stones anyway!! So I need to change this later.
I have some mythic + rings already, but I will also likely keep the circlet for the time being
I think you should wait for a Myth track ring.
To determine the biggest DPS increase for your spec, you should sim all possible combinations of gear in your bag.