Comparison between the Special Edition and the Theatrical Cut(DVD-Version). Both versions are on the Special Edition DVD. The Theatrical Cut on this DVD is basically the Special Edition without the additional scenes. Therefore, it is possible that some of the scenes are different from the Theatrical Cut that was shown in cinemas.
The producers wanted to do something special for the DVD release. That's why they gathered the old team who then created a new music scene. This scene was integrated into the movie extremely well. Nevertheless, the Theatrical Cut remains the version the director wanted the audience to see. The Special Edition is "only" a gift for the fans (and the wallet of the producers). ;)
Running time of the Theatrical Cut: 84:32 Min.
Running time of the Special Edition: 85:15 Min.

Reportedly, one of the scenes was censored for the DVD release, whereas it is said to be in the original Theatrical Cut. This would be the scene at 50:30 min (SE) or 49:46 min (Theatrical Cut). The cloud of leaves which Simba creates here is said to have formed the word SEX (that is if one has a vivid imagination) in the original Theatrical Cut and was thus altered for the DVD release. At Here one can see a picture of the cloud of leaves. However, I cannot verify whether the picture is authentic. If I get the chance to do so later, I will add the info here.

Thanks to WiccanMK for the link

00:00 Min.
The Theatrical Cut begins with the words "In Remembrance of FRANK WELLS. President of The Walt Disney Company from 1984 - 1994", whereas the Special Edition shows the Special Edition logo.
no time difference

09:38 Min.
In the scene where Simba and his father go to the grassland and Zazu flies to them to tell them his morning report, additional footage with music was added. Since it was not possible to integrate the footage into the scene seamlessly some changes had to be made.

In the Theatrical Cut the scene goes as follows:
Zazu lands on a stone and starts telling his morning report. (He doesn't sing.) While he is speaking, Simba sees a grasshopper and tries to catch it. The king notices that and after Simba has jumped against a stone, he wants to practise stalking with him. Simba goes into position and the king asks Zazu to turn around. When Zazu, after some time, asks why he is supposed to turn around, the king explains to him that he wants to practise stalking with Simba. When Zazu hears that, he begs the king not to make him turn around but the king insists on it. A few seconds later Simba comes jumping at Zazu and sweeps him off the stone. The king bursts out in laughter.

Now the Special Edition:
Zazu lands on the stone as well but in the Special Edition he starts singing. The grasshopper has been replaced with a mole. Simba tries to catch it and jumps against a stone. The king notices that and has Simba go into position but he does not ask Zazu to turn around for the practise. During that whole scene, Zazu is singing the morning report in additional shots. After some time Simba comes jumping at Zazu and sweeps him off the stone. The king bursts out in laughter. Up to this point, some of the old shots have been extended or were replaced with alternative material. Now, a whole new sequence follows. Simba continues to sing the morning report. Simba grabs Zazu's tale, waves him around and eventually throws him away. From there on, both versions continue identically.

The running time of the Theatrical Cut is 48 Sek.
The running time of the Special Edition is 91 Sek.
time difference: 43 sec.

83:25 Min.
After the "Special Edition" logo, the credits are different. Some names and categories were added, the order of the text boxes was changed and some new boxes were added, for example for "The Morning Report" song. In order to have the new credits match Elton John's song "Circle of Life" the credits were also sped up. Thus, there is no time difference. The Special Edition ends with the words "In Remenberance of FRANK WELLS. President of The Walt Disney Company from 1984 - 1994"", which are shown at the beginning of the Theatrical Cut.
no time difference