Just saw this thread.
It's a very nice 1914-D. That's a date generally with notoriously mismatched dies and poor strikes. In contrast, this coin has great eye appeal.
Since we know NGC's opinion, let's try to decode their thinking and work through how PCGS might see the coin.

The dies are fairly well matched, EMDS obverse and MDS reverse.

The overall strike is above average for 1914-D, sharper on the obverse than the reverse. The 1913-14-15 Buffs had the weak LIBERTY as an element of the design. On the obverse of this coin, the earlier die state and better than average strike make LIBERTY fairly sharp. The eye, nose, chin, lips, feather tie, date, and second feather are sharp. The rachis and calamus on the second feather are very strong. On the reverse, the tail is complete and split, the horn is sharp, the peripheral lettering is relatively strong, the ground is sharp, but the central design features of the buffalo are average.

Die clashing evidence exists, but isn't prominent, and the dies have not been overpolished.
I adjusted your photos to eliminate the toning. I did this, because I wanted to see the surfaces without being distracted by eye appeal adjustments.
The coin is obviously uncirculated, The issue is the pinpoint grade.
On the obverse, there are numerous multidirectional bag marks in the hair above the braid. There are several SW-NE abrasions on the high point of the cheek. There is a small rim ding at 5:00. NGC clearly saw the obverse as MS-63. I see it as MS-64.
On the reverse, there are a series of bag marks in a N-S line. They begin with a vertical nick in the ground level above "C" in CENTS, and continue with a series of SW-NE nicks running N-S through the front shoulder, and fading as the central design lowers in the hair on the hump. There is a small scratch N-S on the buffalo's flank. IMHO, NGC saw the reverse as MS-64, as do I.
To reach the MS-63*, NGC
appears to have blended its grades and then enhanced the net grade with a slight eye appeal adjustment, possibly for toning.
I think PCGS might see this coin differently, but not radically so. The obverse is on the MS-63/MS-64 bubble. PCGS could go either way here. The reverse is at least a solid MS-64. Where I think PCGS might differ is in the eye appeal adjustment. I think PCGS would rate the strike quality as tipping the balance to the higher grade, and the toning as positive. IMHO, PCGS would grade the coin as at least MS-64 and possibly add the plus designation, for a net MS-64+.
As I said, I'm at MS-64 on the obverse and MS-64 on the reverse. Raw, on a bourse floor, I'd call it MS-64, but expect a price haggle about 1/3 the way between MS-64 and MS-65 to adjust for eye appeal. That's also pretty close to where I think a PCGS MS-64+ would land.
NGC MS-63*? It's definitely on the low end of where this one should land, but not so far off that a resubmission is a lock for a higher grade.
JMHO.