Al B

Well to be quite frank, personally I wouldn't care what stock it's on - *I* would take 016 as long as I paid on a card so I am protected, and have an insurance policy as back up, but that's just my personal opinion. Others are more naturally wary.
If you're going through an agent, then they all have what they call "preferred deals" through certain carriers. This is basically a little something extra in rebates or commissions a carrier will allow an agent if they sell bucketloads of fares/tickets on the carrier. While it's harder on RTW fares to actually do this due to the prorata way the fare is divided between the carriers involved on the itinerary, if your trip includes lots of sectors on one carrier, and that carrier has a preferred arrangement with your agent, then the agent could just prorate the ticket and get a better deal for you.
There are way too many variables in this scenario however, and it depends on how good the agent is or how much your agent cares, not least about you yourself !!

RichardMEL

Exactly as Al B says. Some great agents have been known to save >$200 (or more!) on Star RTW published fares. Others don't care and you get next to nothing.

It might be worth asking your t/a which carrier is their preferred (eg, Fright Centre appears to be far more buddy buddy with QF and I've known some Amex agents to also do special QF deals). If your TA says "well, for Star Alliance I get the best out of airline XX" you could counter that you'd be happy to ticket some longhauls on that carrier (if possible) and that might induce more of a discount.

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RichardMEL, UA 1K
A Star Alliance Member.