according to my little experience,
I think private lessons will be much better.the teacher will focus on you only.
but as you every thing has its advantages and disadvantages.
to me I think the disadvantages are:
2- your teacher will not be able to see you executing technique properly cuz he will be the opponent.
I remember our sensei told me once that he can not judge if the technique is right or wrong if he cant see it from a proper distance executing with another person.
good luck in your journey.