Yes.
When you fly 6000 miles on a Qatar flight on an S fare and credit that flight to Privilege Club you'll be awarded 3000 qmiles.
AA actually earns the same 50% - you'll end up with 3000 AAdvantage miles for this Qatar flight.
When you credit the same flight to a BA account (which earns only 25% on S fares) you'll only receive 1500 Avios.

This is where the whole FFP selection thing gets interesting. You need to compare routes and fares (which airline has good options to wherever you want to go from your home airport, are their fares competitive?) check earning charts/partner earning charts and compare mileage expiration policies.

When you only fly once or twice a year it'll be a few years until you have enough miles in your account to do anything meaningful with them from just flying. Especially for less-than frequent fliers who seek to maximize their points and keep them from expiring, non-flying earning options are especially important. The 20,000 avios sign-up bonus of the BA credit card I was referring to above would give you as many points as you normally earn in over a year, and everyday purchases charged to it will not only add to your account but keep all your points from expiring.

And there's another thing: Are you a single traveller or do you fly as a family or with a companion? If yes, BA offers household accounts where you can pool miles from all members into one account (restrictions apply), and QR offers an even more generous family programme. Bad earn rates look way less bad when there's four people earning...