Here's a bit of observation from recent travel experiences with...

Here's a bit of observation from recent travel experiences with Qantas and Virgin -

Checkin / bagdrop areas
Qantas - The departure hall feels fairly roomy. People seem to move rather swiftly amongst self-service kiosks and there's seldomly any line-ups. Minimal staff required to support all the kiosks.
Virgin - departure hall queues up and without a complete apples to apples comparison (same date / time, same flights) Qantas looks like they could easily handle double or triple the number of travellers while Virgin might buckle if they get any busier than they are now.

Boarding
Qantas - Boarding process is well handled and the crowd moves swiftly. Not sure whether it's the plane, air bridge or whatever, but they get a plane filled quite rapidly.
Virgin - Fairly inconsistent experience. Boarding kiosks don't appear to work as swiftly as the Qantas ones. Takes longer to recognise a barcode and sometimes require multiple swipes.

Inflight Announcements, etc
Qantas - Very consistent including recent changes to the use of hand held electronic devices.
Virgin - Inconsistent experience. On the last flight they seem to have read from old scripts and then had to backtrack to correct mistakes.

Planes
I must have not been on any of the newer VAH planes but the ones I've been on recently all felt rather run down. For 2 flights (737-800) in a row there seems to be a number of seats that can't sit fully upright. Probably end of run due for refurbishment / retirement but they do feel like they're not as well maintained.

Customer Service
Qantas - Think it's been pretty consistent for me and those around me who fly a fair bit.
Virgin - Used to be great. Feeling somewhat less enthusiastic these days.

Lounges -
Qantas - fairly consistent theme at least for those I've visited. Decent selection of things. Space felt well used and comfy.
Virgin - Was quite excited when I first went there as they're new kid on the block but it felt a little bit canteen-like. I know it's difficult to get it right on the first go and they are re-designing the lounges so they may be much better in the future.

Now some observation on the business side of things -

Qantas has been experiencing troubles but I can feel (as a customer) they have invested in making things more efficient. They have to deal with competition and legislations. Qantas has $3bil in the bank (increased to $3bil to the last report as opposed to decreased) with plenty of borrowing capacity untapped. Qantas Loyalty is growing and very profitable. Given their cash position it would be sill to offload QL. Restructure cost money especially when they're up against more than just competitors. I'd say their job is literally upgrading a plane mid-flight and surprisingly kept the plane afloat.   

Virgin on the other hand is cash-strapped. Their move to offload a stake in Velocity is to boost their cash position. People are greedy - no one's going to let go of a cash cow unless if they really must.

Between the two airlines I'd personally have money on Qantas at this point in time.

Most if not all of this is subjective opinions but thought I'd share my 2 cents worth of observation - DYOR.