I myself asked Inagaki Sensei about this matter and here is his answer. I hope everybody will find it useful:
"Jodoshu (A) and Jodoshinshu (B)
by Zuio Hisao Inagaki
Feb. 27, 2008
◇ Though both A and B are based on the Primal Vow, A emphasizes recitation of the Name, whereas B stresses mental state of entrusting to Amida. It may be noted that those who say the Nembutsu do not necessarily place absolute faith in Amida but that those who have absolute faith in Amida unfailingly recite the Nembutsu.
◇ A tends to encourage voiced Nembutsu, whereas B accepts both voiced and soft Nembutsu. B speaks of 'natural' Nembutsu. A 'encourages' the followers to make great efforts to say the Nembutsu.
◇ The number of the Nembutsu recitations is often emphasized in A, but in B the number of the Nembutsu is not important. In B, even one Nembutsu is enough to receive Amida's merit, so long as absolute faith is securely established in one's mind.
◇ In A, even if one recites many Nembutsu all through life, one may not be able to attain peace of mind at the time of death. In B, as soon as one attains absolute faith, one dwells in complete peace of mind.
◇ It follows then that followers of A make great efforts to recite the Nembutsu until death when they expect to meet Amida's coming to welcome them to the Pure Land. Followers of B do not expect this, because they are peaceful and happy in Amida's embracing Light. They feel as if they are always with Amida in the Pure Land.
◇ Followers of B feel the unity with Amida wherever they are. Followers of A do not feel that they are one with Amida. "
After I received this answer, I asked again Inagaki Sensei one question about how to understand the expression “complete peace of mind”. In my next post, you can read my question and his answer.