I would choose for the bitcoin wallet because its much safer in my opinion, also the fact the banks just looking afterwards you.
The bank are also very slow compared with the bitcoin so that is also a reason why the bitcoin wallet is much better.
Yes, I think bitcoin wallets are safer and the best thing is you have your own bank in the form of digital wallet, and which is accessible to you anytime you want, and you can receive/send funds 24/7.
But I would suggest you to have both if optional, but if strictly allowed to choose one, I really will have to take btc wallet, since bitcoins offer much more than bank, and I can use btc more easily than bank money.