The shots that have more exposure (metered at an EI of 800) will have better shadows. When compared with the shots metered at an EI of 1600, their highlights may be just as good, just as good with more grain, or less detailed due to over-development.
It depends on the lighting in the scene.
I tend to pay most attention to the mid-tones. I expect giving them extra exposure will be definitely worth it.
Tri-X has a lot of capacity for latitude. What you do with your negatives is also important. To a certain extent, scanning tends to do better with slight under-exposure, and optical printing tends to do better with slight over-exposure.