Had Picard been on the NX-01, there would have been peace with the Klingon Empire from the beginning, all of Earth's first contacts would have been handled with dignity, composure and respect, leading to multiple peace treaties, which would have seen the Federation formed by the beginning of Season 3.
Had Kirk been the Emissary, then Opaka would have been some 20-something blonde in soft focus who he would totally bang. He'd then unleash Kirk Fu on the Prophets who would go back in time and erradicate him from existence.
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)