Nice coin. The 1937-D three-leg is one of the more difficult coins to grade because both dies are heavily abraded, the abraded dies emulate circulation wear on mid-grade coins, and all three major TPGs approach the grading differently.
Your coin has an average strike for the variety. It is a mid die state coin that was struck after the second die polishing severed the third feather. It clearly is a nice upper mid-grade example.
The obverse shows more detail on the second feather and hair braids than most VF-35 examples. The second feather rachis and calamus are nearly complete and the braids have more separation than a VF-35. The weakness on the lower feathers and ribbons and the "floating" third feather are due to the die clash polishing. By itself, the obverse should make EF-40.
The reverse is consistent with VF-35. The clash polishing was more severe on the reverse. Technical grading cannot focus on the buffalo's head, horn, upper back, foreleg, or rear legs for obvious reasons. For borderline VF-35/Ef-40 coins, that largely leaves the buffalo's flank and the four points of rim contact as the distinction. This is where I strongly part company with PCGS. If the buffalo's head, tail, the "F" of FIVE, and "S" of CENTS are starting to merge into the rim, the coin should grade as VF. Here, the head is just separated and the "S" of CENTS is close, but minimally separated. The tail has started to merge, and the "F" of FIVE is merged.
IMHO, this is a VF-35/EF-40 bubble coin. If they ever adopt my wished-for intermediate grades (F-18, VF-38, and especially EF-48), this coin would be a poster coin for VF-38. In the absence of a VF-38 grading level, the reverse has to be considered VF-35.
On balance, given current grading levels, this currently is a high end VF-35. The first
TPG to adopt VF-38 as a grade level wins, and this coin would notch in at that grade.
PCGS frequently bumps these coins to EF-40, wrongly. (They regularly undergrade F-15 and VF-20 Buffs and regularly overgrade VF-35 Buffs.) NGC struggles in general with grading mid-grade abraded die variety Buffs. ANACS currently does the best job grading Buffs, effectively differentiating among strike, die wear, clash polishing, and circulation wear. (That wasn't always the case with ANACS, and their older grades for Buffs are an adventure.)
Again, nice coin and a great example of the variety.