Unfortunately, there are not only differences between the theatrical version and the Director's Cut, as this censorship report shows, but also differences between the Director's Cut versions themselves. Several versions miss blood splatters in a few scenes.
The following versions were checked:
US-DVD (Theatrical version and Director's Cut) missing blood splatters
German Blu-ray (Theatrical version and Director's Cut) missing blood splatters
English Blu-ray (Theatrical version and Director's Cut) missing blood splatters
German DVD (Director's Cut only) containing all blood splatters
The most plausible reason for the missing blood splatters is the use of seamless branching. In this technique, two different versions are not stored separately on a DVD or Blu-ray, but identical parts are stored once and the differing parts separately. When a variant scene comes up, the respective is chosen and then it jumps back to the identical main part. The viewer normally does not notice this jump.
Should seamless branching have been the reason, then the producers of the DVD or Blu-ray have either forgotten to build in the alternative image in the below-mentioned scenes or have ignored it willingly, since they considered it unimportant. It always involves only a few frames, which differ minimally. The runtime stays constantly the same.
Besides, this is not the first case of this kind. The Unrated version of Alien vs. Predator 2 on Blu-ray differed from the Unrated version on DVD in two short shots. Here, too, the (more harmless) footage of the theatrical version was shown in the Blu-ray version. The cause of that was a lapse concerning seamless branching, as well. As of today, the mistake has not been corrected. You can find a report on that here.
Meanwhile, there is blood at the proper places in the Director's Cut, even in the seamless branching version, wherever it was missing in the theatrical version. But still, there was always a brief cut shortly before or after that.
Mistake or intention? Annoying or unimportant? Everyone has to decide for himself. The possibility of a deliberate censorship of the blood splatters in several versions can probably be ruled out, however.
The differences between the theatrical version and the Director's Cut, as well as many information on the genesis of the film can be found in a separate censorship report.
The seamless branching versions miss blood at 10 parts of the film. The upper picture is always from German DVD, while the lower one comes from the German Blu-ray.
Robert Loxley slays an enemy.
Robin's arrow only touches Godfrey lightly.
The debt collector in York
A monk is slain.
Fight in Nottingham
A villager is slain.
Two servants are slain in Loxley's castle.
Robin slays a Frenchman.
And another one.
At the beach
Robin bashes an enemy on the head.
Godfrey slays an Englishman.
Brother Tuck slays a Frenchman.