I have flown several times over the past few months with both of them, to/from HKG to LAX, SEA and JFK.

Some things to consider:

- EVA Premium Economy is great for the price. OZ does not offer anything comparable. Took it last year.

- Only flew in J on the most recent trips: Service is equally good. OZ was a bit more attentive on all flights, but that's complaining on a very high level. Planes are equally new and clean. Seats are similar.

- If you have lounge access, I'd probably go for EVA. Their TPE lounges have much better food options. Walking distances are usually shorter for connecting flights at ICN than they are in TPE. But again, no dramatic difference.

- At least during transit, I never noticed anything out of the ordinary and wouldn't factor in the MERS situation at all - especially since they officially announced the epidemic over a couple of days ago.

- Focus on flight and connection times and price...you can't make a wrong choice between these two airlines. Both are equally great. If you can get Premium Eco on EVA, choose that one.