If two engine oils have the requisite OEM approvals and one has a higher initial TBN than the other, which one is better for use?

higher TBN is not always good for the engine

it depends on the diesel if it is high sulfer or not

in normal conditions use the regular TBN rate so u wont have resdue 

Good point by Radwan. As for Abdolrahim, don't you think TBN retention characteristic is more important instead of the initial TBN?

If the engine oils have the same grade it's better to use with the higher TBN. Because of S componenets pollution in the fuel affect on oil and reduce its TBN, now if we use oil with higher TBN, oil would have long life in engine.

If the Sulphur content of both fuels is the different.

then for higher Sulphur content fuel the Oil with higher TBN is preferred.