I've flown to Europe in J with several airlines, which I would rank in the following order:
1 Singapore
2 Etihad
3 Qantas
4 Malaysia
5 Air France
6 Lufthansa
For me, the top three are all a fair bit ahead of the others because they have proper flat beds (not on all flights with SQ or QF - but you can check this before booking).
Two things I particularly like about Etihad are (1) all seats have direct aisle access, and (2) they have a dine on demand service, meaning you can eat anything on the menu at any time during the flight (I haven't seen that with any other airline in J). Etihad is also usually the cheapest out of the three, plus they service more destinations with just one stop (although QF may have caught up now with the Emirates alliance). Etihad and QF provide chauffeur pick up/drop off, which is nice, but you could just pay for this yourself if you travel with another airline. Singapore and Etihad both provide truly outstanding service - a fair bit better than Qantas IMHO (which is not to say QF is bad). Singapore just about wins top spot on my list for having awesome, very spacious seats, and one of my favourite lounges in the world (the Silverkris lounge in Changi).
There's not much to separate Malaysia, Air France and Lufthansa. And just to stress, even though Lufthansa comes last on my list, it's still good (I've ranked it below MH and AF simply due to lesser quality of food). Plus, if you buy a Lufthansa fare, you will be on Singapore metal between Australia and SIN, and you still get into that great SilverKris lounge. So if it was me and I got a good deal on any of the above airlines, I'd be happy to take it.
I've also flown transatlantic in J with BA and I thought it was on a par with Qantas. I assume they would be similar or better on a longer haul route. I'm flying J to Europe with Thai for the first time soon - from what I've read it will rank somewhere close to numbers 4-6 above. I haven't had the pleasure of Cathay Pacific in J, but I've heard only good things (mind you, the same was true of their Y product but I was disappointed when I experienced it).