I was searching thru the information here, but I am still not clear for me what the best strategy for me is.

I travel mainy on RTW tickets (3 or 4 per year), OW and Star, all in F. For the flights in between I try to get award tickets, also in F.

I like the LH program, because it gives 3.75 x miles in F. So a typical 29 K Miles RTW gets more than 100 K miles - and that is enough for an USA-Europe F award.

The oneworld miles go into my AA account. Because of the changes there (miles conversion of the 500 miles upgrades has changed) AA gives 2.5 times miles flown in F, also the awards between US and Europe are more expensive (and you get them only on AA, which is inferior to many other airlines in F).
So i am thinking of changing to BA or CX, hoping that F awards would be easier to come by.

So please let me know what you think.

I had a similar decision to make, and ultimately I chose QF. BA is almost as good as QF (the differences are complicated so it really depends on the routes you fly whether there is a difference). CX has a much less generous FF plan, it is good only if you benefit from their top-tier status (and the ticket availability guarantee).

I agree. I have kept AA EXP (for now), but last year qualified for Emerald (Platinum) with QF. Mileage earning is not quite as good as AA - i.e. you don't get the 100% bonus on all oneworld carriers (Just QF & AA I think). The cost of awards and flexibility is also not as good as AA but you do get transatlantic earning and redemption with BA and free Admirals Club access on domestic North American itineraries.