I was looking at this also (potentially doing the same trip next year) on qantas.com.
The AS metal flight LAX-SEA (and vice versa) when booked on the AS flight number books into F class regardless of booking "Business saver" or "Business". When booked on the QF flight number, it books into I or C class depending on your fare type.
Both AS and QF flight numbers will earn the standard base rate of QFF points (1 pt = 1 mile travelled) and a 50% cabin bonus. MileageMonkey says 956 miles so that will be 956*1.5 = 1,434 QFF points each way, not including any status bonus.
Frequent Flyer - About the Program - Terms & Conditions
You will earn F SCs (90) for the AS flight number and J SCs (60) for the QF codeshare.
The dates I'm looking at show the same price for either option, so going for the AS flight number will give you an extra 30 SCs. One potential downside is if you are going for P1, those 90 SCs will not count towards your required 2700 with QF flight numbers...
Interestingly enough if you book the whole MEL-LAX-SEA on a discount Y or PE fare, you will earn full Y SCs (30) and 956 points on the AS flight number but discount Y SCs (15) and 956 points on the QF codeshare. Yes, discount Y earn when booking and paying for premium Y. Again, where both options were possible for the same AS flight, they were the same price.