Let me see now. Hmmm.
Well, Jesus died for our sins, lao-tzu did not.
Jesus rose from the dead just as He said He would. lao-tzu is still dead.
If you want to know more, perhaps you should read about the life and times of Jesus Christ as recorded by 4 of his close followers, Matthew, Mark, Luke and John.
I think their philosophies were similar. Both were very loving and peaceful. Lao Tzu is very concerned with yin and yang, the balance of good and evil, black and white, etc. But Lao Tzu was more concerned with inner peace as a way of bringing outer peace. Jesus would have you look to himsef/God to find peace. Jesus started a religion, as did Lao Tzu, technically. Although Taoism is not linked to a specific God, so you could be a Taoist and anything else as well. You don’t worship Lao Tzu, he just had amazing ideas on how to make the world better.
1) Both were key figures which promoted a spiritual movement.
2) Both offered a path toward self-development and spiritual advancement.
3) Some of the teachings of each hold similar aspects as far as personal conduct.
However, once you start getting into the specific ideologies, one is bound to find more differences than similarities.