The old estore was not very well integrated with ba.com and required you to log-in again even if you were already signed in to BAEC. The new site has better integration which avoids the need for a double log-in. It also welcomes you by name.
There is also a reminder on the site about which retailers accept British Airways American Express cards.
I couldn’t see any signs of any special offers to promote the relaunch, but I would expect something to appear as we head into the main Christmas shopping period.
The link to access the store directly is shopping.ba.com