The D-44 85 mm divisional gun had the same ballistics as the S-53. Despite being designed in 1944, it did not enter production until after the war, but these tables can grant us some insight into how well the T-34-85 could shoot.
This table describes the blunt tip APBC round BR-365. The muzzle velocity of this round is 800 m/s, and its flat shot range for a 2 meter tall target is 950 meters, 1090 meters for a 2.7 m tall target and 1150 meters for a 3 m tall target. The columns of the table are as follows: distance, three settings for the sight, trajectory height, two columns for various corrections, one column with the change in impact height for one division of the sight, the angle of the gun, the angle of impact, impact velocity, time of flight, and then finally, the two columns we care about, vertical and horizontal mean dispersion. As you can see, the dispersion is only 0.2 x 0.3 meters, which is very good, but not quite as good as on the pre-war U-10 design.
Next we have the BR-367 APCBC shell. Its ballistic properties are almost identical to the BR-365, but it flies a little faster (805 m/s) and is a little more precise (dispersion of 0.2 m by 0.2 m at 1000 meters).
Here is a table for the sharp-tipped BR-365K AP round. Much like the APBC round, it has a muzzle velocity of 800 m/s, but a greater dispersion of 0.3 by 0.4 meters at 1000 meters.
Next is the BR-367P (APCR) and BR-367PZh (APCR with a metallo-ceramic driving band). These shells fly faster than the AP shell, at 1020 m/s, and thus have higher flat shot ranges: 1140 m, 1290 m, and 1350 m. The table columns are a little different, as the sight correction columns are missing. The rest of the columns are the same. These rounds are a little more accurate than the AP at 1000 meters, deviating 0.2 meters in both the horizontal and vertical on average.
This is another APCR shell, BR-365P. With a muzzle velocity of 1050 m/s, it flies a little faster than the BR-367P, but pays for that with reduced precision: a deviation of 0.4 meters by 0.5 meters at 1000 meters. It also loses speed faster than the BR-367P.
Last but not least, the table for O-365K and O-367A HE rounds. This table has a lot more settings, since you care about a whole extra dimension when shooting HE. The first column is, as always, range, then three columns for sight settings with an uncapped detonator, followed by two columns of corrections for a detonator cap and a metallo-ceramic driving band. After that is trajectory height as seen above, but the rest of that page is various corrections for wind, temperature, etc. The first column on the second page is the change in distance corresponding to one one-thousandth change of sight settings, the size of a tight bracket in thousandths, the angle of the gun and angle of impact, impact velocity, time of flight, and finally the dispersion. At 1000 meters, the depth-wise dispersion is 14 meters, the height-wise dispersion is 0.2 meters, and the width-wise dispersion is 0.3 meters.