I'm comparing the cost in miles and fees for an award flight from DCA to LHR. There is a single flight number AA flight (AA 104) that stops in JFK and switches to a 777. What are the opinions to the better use of miles for a Y ticket?

AA - 30K miles + $5.60
BA - 20K miles + $180 (taxes + BA surcharges)

That's not much difference. The issue could be if there is a need to cancel the ticket. On AA, I get my $5.60 refunded, but pay $150 to redeposit the miles.
On BA, the cost is paid fees+surcharges - $55. But are all taxes/fees refunded? The BA site is a bit unclear to me.