Oddly, right from the beginning of his era, the 10th Doctor’s brown suit jackets had two subtly different back styles.
The first had the upper center back seam between two pinstripes, with the two back pieces cut on a slight diagonal (so the pinstripes were angled slightly downward toward center in a V-shape, instead of vertically).
The other style had the upper center back seam on a pinstripe, with the two back pieces apparently cut so the pinstripes draped vertically:
The difference between the two back designs is more easily observed when they’re side by side:
Unlike the different collar styles, the contrasting styles of the backs didn’t appear to simply be a case of early version/later version of the suit, since both styles were consistently seen throughout Tennant’s first season.
However, the second style back, appears to have been the preferred one; I never directly observed the first style after the season three, whereas the second style lasted through the remainder of Tennant’s era (including his appearance in “The Day of the Doctor”).
Also note that both versions of the brown suit had a tapered backs, as tailored jacks often do. (That is, the center back seam line was taken in via a gentle curve moving downward toward the waist and small of the back.)
The lower back of the 10th Doctor’s brown suit jacket had a single vent at the center back, with the back left overlapping the back right by four pinstripes past the fold (which was, itself, on a pinstripe).
It is worth noting, however, that at least one of his brown suit jackets’ vents might have had a narrower overlap, but it’s difficult to say for sure …
At the top of the back vent was a waistband, which was self-fabric cut on the crossgrain (i.e. the pinstripes were horizontal).
It spanned the entire back, from one side/back panel seam to the other, and it was simply edge-stitched onto the back of the jacket body along the upper and lower edges.
This back waistband was a nice touch for a suit based on one from the 1930s.
You can see similar back waistbands on other garments in projects which take place during that era, such as Indiana Jones’ and Belloq’s jackets in Raiders of the Lost Ark (which took place in 1937):
The back waistband appears to have been cut with unusually large seam allowance – something in the neighborhood of 1″, as evidenced by the impressions in the screencaps below:
The back waistband was positioned slightly higher than the “faux-flap” pockets.
On every brown suit jacket I observed, the back waistband was a consistent height of approximately four (horizontal) pinstripes, with the upper and lower edges being between pinstripes for some reason … curious, considering the same approximate height could have been achieved with the upper and lower edges being on pinstripes …