Were some of Jesus' disciples more privileged than others? Mark 3:14 Then hit selected twelve of them to be his regular companions, calling them apostles.*He sent them out to preach, and gave them authority to cast out demons. NLT
Mark 5:37 Then Jesus stopped the crowd and wouldn't let anyone go in with him except Peter and James and John. NLT

And other occasions.

Mark 9:2 six days later Jesus took Peter, James an John to the top of the mountain. No one else was there. NLT
Mark 14:33 He took Peter, James and John with him, and he began to be filled with horror an deep distress.

Is there an sacred/specific reason why Christ only let three of them go in with him an not all twelve?
Why did he take just Peter, James an John to the top of the mountain? At the olive grove called Gethsemane. He told everyone else to sit here while I go pray....Seems to me he favored these three?
Did some disciples get treated differently from others?

You've pretty much answered your own question here. Jesus had many disciples. At least seventy, probably many more. And different groups were certainly treated differently. The best-known select group were the Twelve, called the Apostles. They were given more detailed explanations of some of Jesus' parables, and other insights not given to others. Within those, Peter John and James were selected to be present with Jesus at specific intimate occasions, including the Transfiguration and the raising of a little girl from the dead. Those three would go on to be leaders of the church.

Is this favouritism?

I think that's your implied question. To see that, you really have to look at what it means to be selected. The Twelve, and within that group the Three, were intended to be leaders of the church. If you look at what Jesus means by leadership it is "to become the servant of everyone". The Twelve suffered and were all persecuted, and tradition has it that all except John were martyred. You can consider that 'privileged' if you like, but it's not a privilege many of us would jump at.