Sounds like you really enjoy your APs, which means we have a lot in common!
The direct answer as to which of those 2 is more sought after is the End of Days.
But I always recommend you purchase the one you prefer, the one you anticipate will bring you more enjoyment. Your 2 other APs have large cases, and in that regard the T3 is perhaps a better fit for you (especially if you prefer wearing these big pieces).
The EOD will wear much smaller, as it is in the 42mm Offshore case and is all black. If you are OK with this size difference, the the EOD is definitely worth exploring. I feel the market on this particular watch is softer than it has been in previous years, meaning it is a good time to find one. And wearing the End of Days evokes a feeling beyond description. It would certainly offer you a very fresh take on Audemars Piguet.
Just because, some photos