BA don't try and compete with the Middle Eastern carriers when it comes to F - and if you talk to senior staff they'll tell you as much.
Their F product needs to be on a par with other carriers running the direct westbound routes - and it largely is. IMHO it sits above VS Upper Class and Delta One, and whilst the seat is cool in AA F - the service is generally meh. So BA's F product is the choice for most when going direct from LON to the USA. That's all they're really concerned about.
The fact you can have showers in the sky and caviar and £300 bottles of red on the GCC carriers is not something BA are trying to emulate. And the price typically reflects that too.
So yes, if you're going East I'd suggest paying for whichever airline you feel offers the best price and product on your route. Westbound, there's not a lot of choice I'm afraid.
There's a reason BA has been unable to shake off the quip that their First product is "the best business class in the sky".