I know this is going to be laughed at but I have a strongly held impression about these two seats and the apparent coveting of them.
It's because they are blanked out until -72hours.
Or simply that "1A" sounds like the most impressive seat, with or without any blocking by BA.
But, apart from the well-known munter factor, I do think 1K is a great seat on a 747 (a subject which has been done to death, I know). Whereas when I took 1K on a 777, it was only because virtually everything else was gone.
It's a horrible seat.
If you find yourself stuck in 1K, and I'm in 10K or 15K, then I'll relieve you of your misery by swapping. I really think calling it "horrible" is a tad OTT.