Moderator, this thread is all about choosing between OneWorld airlines, so perhaps it should be moved to the OneWorld forum?

Use what points/miles? (Do you have tons of hotel points or something else that can be transferred to Cathay or whoever to "jump start" your account?) You didn't mention how long this trip is, but your points/miles won't post until at least several days after each flight, most likely. And you won't earn enough for an upgrade untill well into your flight, quite probably before it's all done, if you have no "jump start" to your account by transferring in from somewhere else.

Secondly, you can typically only upgrade on the airline you earn points/miles with. So if you earn with Cathey, you can't upgrade on Qantas, or vice versa. If your goal is to upgrade with Cathay, you have to collect with Cathay! But first figure out if this will work, because if you won't collect enough miles to qualify for an upgrade before you return, then there won't be a big point to choosing Cathay, and instead you want to choose whichever program will work best for you long term.

OTOH, even though you say your flights otherwise tend to be within Europe, beware of BA (presumably your "home" OW airline, since you're flying out of and back into LHR?) giving only 25% of miles flown on cheap economy fares, and I think Iberia may only give 30% in those cases.

So you need to first ifgure out how many miles Cathay will give and how many miles Qantas will give for the fare code (an alphabetic character) that your tickets are in, which may in turn vary depending on the program you decide to join (ie, Qantas may award a different number of miles to its own members than to Cathay members for a particular Qantas fare code, etc).

You even need to figure out if you will earn miles/points at all! If by "Qantas deal" you mean some special package, some such special packages don't give you miles at all! (Even if it's a trip booked "the normal way" at Qantas' website, you still may have certain portions, especially certain flights within Australia, which might not earn points/miles.)

Don't rule out OneWorld airlines you're not flying at all, like American. The reason: With some airlines in Asia (or even mainland Europe, like Finnair) your miles expire after a few years even if you keep earning new ones. If you don't fly enough (or on expensive enough fares) to earn enough miles/points to use them within a couple years each time, it may all be a waste. But US airlines (and AA is the OneWorld airline in the US) don't let their miles expire as long as you have "activity", and every way of earning or redeeming miles counts as activity.

(So research the expiration policy of each OneWorld arilne you're left with, after factoring in how well or badly each treats people who buy cheap economy fares.)