You should generally apply to the German representation (consulate or embassy) competent for your place of residence.
While you said you are a resident of India, if you already entered the Netherlands on a MVV, it would probably make you a resident of the Netherlands for this purpose (you would certainly need to register in the Basisregistratie personen). You should therefore be able to lodge your application to the German consulate general in Amsterdam if you want.
On the other hand, if you are still in India, you should apply there and the MVV would not make much of a difference. You cannot use the MVV to enter Germany and then apply for a long-stay visa. While a Dutch visa/permit does allow you to visit Germany, directly applying for a residence permit within the country is only allowed in some limited cases. As Indian citizen, you need to secure a student visa before entering Germany (so either in the Netherlands or in India).
Generally speaking, the process should be similar in the Netherlands and in India. One difference is that the consulate general in Amsterdam is probably smaller (not that many Dutch residents need visas for Germany) and does not use any third-party company to handle applications. You have to call the consulate directly at specific times to make an appointment (information here, unfortunately only in Dutch or German).
As far as documentary evidence is concerned, the German consulate will probably want to see either your MVV or a proof of registration (or uittreksel uit de BRP) to establish that you are a resident in the Netherlands. Otherwise, the requirements should be similar.