Have I figured out how the code shares work?
 

If I book a ticket on Cathay Pacific from Los Angeles to Singapore, leaving LAX on March 22 and leaving SIN on March 31, in Discounted Economy, the price is $923.03, which is a Class M ticket. I will get 25% of the miles with BA and no miles with AA.

If I book a Y class ticket (Economy) for $3813.03, I will get 100% of the miles with AA.

I assume the seat will be the same and most important, so will the beverages.

Do I have it right?

No, you need to take Codeshare 101 again. You described partner earning rates. A codeshare is when there's an AA flight number assigned to the CX metal. Which there is in that case, by the way.

If you want full AA miles riding on the CX flights you'd be overpaying if you shelled out 3 grand for (anybody's) Y class tickets. You can ride in M for $1500 or so, do the Platinum challenge and come back an elite with around 25K miles in the bank. Is platinum status and a free trip's worth of miles worth the extra $600 or so? Hard to say.

I punched in your dates on aa.com. There are many connections with AA-only numbers, starting from about $1,000. Most fly AA to Tokyo, then connect to Japan Airlines.

If you want to fly CX, they have a LAX-HKG-SIN itinerary all on CX metal, and AA flight numbers. About $1,400. Fare code is "H". You earn 100% AAdvantage miles and 1.0 EQP per mile flown.

Now, please sent me the $2,400 I just saved you.

Oh, actually, total price with tax is $1,550.60 for that itinerary:

AA flights 6089, 6107, 6108, 6122. All CX-operated.

Before I send you a check, will I get 25% of the miles with BA if I pay $923.03?

$627.57 for frequent flyer miles. That does seem like a lot of money.

I would lot to experience Cathay but don't think I could survive American in coach for a flight like this.

Right, you earn 25% BA miles but zero Tier Points for Executive Club, on a CX "M" fare.

It's up to you to decide what's more important. Paying $600 more may make sense for at least 17,000 AAdvantage miles and 17,000 EQP. If you're AA elite then you get bonus miles too; and/or you can use this for some challenge to get higher elite levels.

That compared to earning <5,000 BA points and does nothing for your Executive Club status.

BTW, wally, CX's Y-product isn't that special, and seating on the 744 for LAX-HKG is pretty tight.

If miles and elite qualifications aren't that important, seriously consider taking SQ's non-stop with "executive economy".

A roundtrip on SQ's executive economy nonstops on those dates would cost USD 1,654.63 for their Flexi fare. To get a Super Deals fare would be in regular economy with a connection. Via Taipei it would be USD 1,089.63

If you type the dates into Sidestep, you see the discount economy price. This does not show up on Kayak.