This is always an interesting question.

I think the answer is a mix of all of the above.
BA F is better than BA J. I don't honestly think you could say it's the same or worse. The seat is 50% larger overall (most airlines work on 4 Y seats for a J seat and 6 for F) and the food and wines are better. Amenity kit is better and you get pyjamas and turndown service.
The question is to what extent it's better than J and then how BA J and F rank in the market...

The key on my view to understanding all of this is BA J. This is because BA J is unique and no other airline can have the BA J layout of yin-yan as BA has the patent. This means it can get many more J seats in a given floor area. In my view BA is highly unlikely to give this up - I suspect that even the next iteration will have this but allow direct aisle access as if you see the feedback that is the main gripe with the current BA J. This then of course allows BA to do high levels of discounting in J with large clients and still turn in a tidy profit. That's why they have stuck with it and they will do so. Also many have less freedom then they espouse on here - I know some will flame me on here for that but most corporate deal policies are increasingly strict and the deals that are struck are dependent on a set amount of volume.... This super high density then is also partly why you have aircraft with 50, 60, 70 and even 80 J seats (outside the A380 which is for most airlines a niche aircraft only only a handful of trunk routes). It can discount heavily and still fill J and make a profit.

There may well be other airlines that have a nicer J but the discounting is probably less heavy and look at the sizes of the cabin - it's often 30-40 seats even on their largest planes. That's simply because they cannot get close to BA J operating margins and costs. So they have gone for a better product but many less seats and less deals so they can fill a smaller cabin overall at higher prices and turn in a profit.

For BA F they have gone for something better than J that they think is the balance between more luxury but that they can fill with paying passengers on a wide network of routes. Note the key here is paying passengers, not POUG at the airport or Avios 2-4-1 etc. Paying passengers are what they care about and F makes no money on nearly all routes (hence for the 789 it's a smaller cabin). This is different to nearly everyone else who have either ripped F out altogether or it is a very small cabin only on a few trunk routes. The mighty CX which people talk about has only 6 F seats and only has F now on around 10-15 routes. TAM ripped out its F of 4 seats only 1 year after it introduced it. AF has a very luxurious offering but the price is way, way higher. BA have just decided that from London and their other main routes there is a big enough group of people willing to pay more than J for something a bit better but that the prices of AF are not going to work for them.... As someone mentioned with Etihad you can have a huge personal suite, but only on the A380 and its 20,000 each way..... There just aren't many takers for that kind of service.

So the reality is that BA is the middle of the road in F as a result of J. I am pretty sure that J is due a refresh and suspect that it will be direct aisle access. This will work will as it still gives BA the edge on profitability per seat and also keeps up with market trends. On the A380 it will cut down the number of Y seats which is BA's biggest problem with the A380 - 300Y seats just done sell...... BA F is likely to stay roughly where it is - it's clearly what the market that BA targets for paid F are happy to pay for something a bit better, and for BA's decisions about BA F it's only the paying passengers that will feed into that decision - no-one else.

FD.