There is only ONE LIVING GOD and He is the Lord Jesus Christ. Christ is the only One who is Prince of Peace (Isaiah 9:6) and don't forget that Buddha was merely a human being, created by God, but Jesus Christ IS GOD.
Buddha is dead like every other human being. Jesus Christ the Prince of Peace is ALIVE.
Therefore, logically, Buddha who is dead,cannot give you peace. Whereas Jesus Christ who is the LIVING ETERNAL GOD is the only One who gives life and peace and salvation to all who will believe, trust in Him and obey and follow Him
When Christ died temporarily, before He rose from the dead, He left His Peace with us. (John 14:27) and He told us all things in the Bible leaving us with His Holy Spirit who reminds us of all the things Jesus told us, SO THAT WE WOULD HAVE PEACE (John 16:33)
When we preach peace, it can only be through Jesus Christ, because He is Lord of all (Acts 10:36)