I’ll choose BALL. It looks more refine and versatile to different occasions. Not a fan of BB41, case side profile is too bulky and thick.
I wouldn't have bought either in the first place. But I suspect that's because my taste in watches is very different to yours. Which renders my opinion useless to you.
This may help you decide.
Get a coin. Heads sell the Ball, Tails the Tudor. One flip, no second chances, no going back on the outcome.
Do not read any further until you've flipped the coin.
Hmmn, I said, "Do not read any further until you've flipped the coin." this won't work unless you do so.
OK, either you've flipped the coin, or there's no helping you. Assuming you have flipped, think back to the moment the coin settled. Did you feel disappointment of relief? If it was relief, go with the coin toss, if it was disappoinement, ignore the result and sell the other watch.
If you really want the opinion of random strangers on the internet, here's mine. Asking the opinion of random strangers about your trinkets is pointless, unless of course you wear the trinkets solely to gain the approval of random strangers (in which case I recommend selling both watches and spending the money on counselling!) It is you that has to wear these, they are for you to enjoy and you should not give a stuff about the opinion of anyone else.
Of course that's just my opinion...