The tests are almost identical when it comes to the actual welding and prepping of the coupons.
I do the same thing, when I test my guys, I make sure they meet the stricter D1.5 requirements, and I write two different certs for them; one for D1.1 and the other for D1.5.
The size of the coupon is the same and joint, and the big difference is you can't use power tools on the bridge test, hand tools only.
If I were the person writing the OP, I would tell him to go for both, it only increases your chances of employment and makes you a more valuable employee. There is nothing shady going on if all the requirements are met for both codes.