Update: Christian Science and the Bible Students movement were started at about the same time.
https://en.wikipedia.org/wiki/Christian_Science says that Eddy began teaching her first student in 1866, that in 1875 she wrote her theology book called Science and Health with Key to the Scriptures, and in April 1879 she and her followers founded her church. Eddy died in 1910.
https://en.wikipedia.org/wiki/Jehovah%27s_Witnesses says Russell formed a Bible study group in 1870, in 1876 Russell and Barbour jointly produced (another source says published in 1877) the Three Worlds book, and that in July 1879 Russell began publishing Zion's Watch Tower. Russell died in 1917.
The Wikipedia article about Christian Science says the following. 'In 2010 the New York Times reported church leaders as saying that, for over a year, they had been "encouraging members to see a physician if they feel it is necessary", and that they were repositioning Christian Science prayer as a supplement to medical care, rather than a substitute. ... In 2021, a church Committee on Publication reiterated that although vaccination was an individual choice, that the church did not dictate against it, and those who were not vaccinated did not do so because of any "church dogma".'
Similarly, we know that though the WTS for a period of time forbade organ transplants and vaccinations they later said such are a conscience matter. They had also forbade blood fraction for a period of time but later said it is a conscience matter in regards to many blood fractions.
The membership of Christian Science is in decline (at least in the USA, where it like the WTS was founded in) for the Wikipedia article about it says the following. "Christian Science became the fastest growing religion in the United States, with nearly 270,000 members there by 1936, a figure that had declined by 1990 to just over 100,000,[8] and by 2009 reportedly to under 50,000.[3]"