The similarities between the spread of Christianity and Buddhism is very slim, they both started as origin stories (same with the Indian stories) and quickly formed into religions. Buddhism originated in northwest India while Christianity originated in Judea, a roman province. They both spread throughout the world and became many state religions. The differences was that Buddhism was spread by monks while Christianity was spread by preachers.
side-note: (I noticed that this has been sitting here for a while so I decided to answer it for you ^v^)
