I prefer a foot in each camp. Gives me flexibility. I don't like being tied to one program or another. They both kind of have their pros and cons like any program.

In terms of a status match you can submit your Air NZ activity statement to their frequent flyer email. Use the last 6 months at least, you can do 12 months. They may offer you a tier accelerator challenge. eg get gold if you earn 200 status credits in 3 months or platinum if you earn 400 status credits in 3 months. And no, the DSC can't be used for the challenge. But it's at QFs discretion if they offer this to you but there's a reasonable chance if your flying pattern matches their network.

There is no equivalent of recognition upgrades in the Qantas system. You can use points to upgrade and you enter the lottery with everyone else. If you're platinum you can call and request the release of award seats but I think its when they have sale fares and there may be some other conditions eg outside of peak travel... I can't remember them all, I've never bothered with it before as I rarely fly QF longhaul. I don't know what your chances are of getting 4 upgrades from Y to PE. Make sure you're on an A380 I guess. Being NZ based you don't have the same ground earnings opportunities that everyone in Australia does. I don't have a Qantas earning credit card and whilst I do use everyday rewards cards at Woollies in Oz I'm pretty useless at checking out when to use boosters etc. I swipe my card at the BP station so I collect extra where I can but ... you'll never earn what they earn. Redeeming Qantas points they have large taxes, there are Classic rewards and classic plus rewards (for super points rich people). Anyway, I don't particularly value the Qantas points and rarely use them but when I do use them I am happy with their uses. I think I flew a friend to NZ, used them on domestic to visit a friend as regional flight was astronomical and once LAX-SYD to get from PE to business, and redeemed for Qatar J to Europe although not sure what that availability is like these days. It's easy to keep status if you use the Double Status Credits offers usually around Feb or march. I think there are a lot more QF platinums, platinum ones and chairman members than NZ Elite and EP1 so... there's a lot more competition for upgrades. I don't think they get approved straight away like some of the Air NZ ones do quite far out. I hardly use them but I quite like the ability to use EAPD to go from Y to PE confirmed immediately. I prefer this over the QF system. But also at least with Qantas you don't lose your RUs because you use points for upgrades and if unsuccessful then the points stay in your account. You need activity every 18months to keep points from expiring.

In terms of other benefits I guess the F lounge access departing Mel, Syd, LAX if platinum, the Auckland lounge will become a one for all lounge whenever they decide to start on that. Then there are the other OW F lounges. You have earlier access to award seats than gold members. Access to domestic business lounges if that's part of your travel patterns. Whilst I've done very little long haul with QF, I think NZ's food is a bit better in J and PE. I prefer the NZ PE seat over QF. And the lack of wifi internationally peeves me off with QF. Also I don't think you'd like to get stuck with economy on Qantas unless it's an A380 or A330. Which is why I think VA has its place in Australia and prefer their economy seat over QF on the 737s. The neighbour free seat is not guaranteed, but at least you'll get refunded. You can buy a twin seat at a lower cost (without taxes) and earn status credits for that. Apart from JFK it's a bit of a pain to fly backwards to then fly forwards to North America. Asia is ok, but there are other carriers you may prefer on certain routes which is why a number of Qantas frequent flyers don't fly Qantas internationally. The rusted on loyalty types do, until they get burned in some way then they swear off Qantas. Qantas aren't particularly cheap either. The option for lifetime status is nice to achieve. I'll go for gold but not lifetime platinum. Not achievable with my patterns. But it's nice to have something to fall back on in the long run.

You can probably maintain a foot in each program. Up to you to decide which level that is at.