There are definitely more hydrogen atoms in a mole of water than stars in the Milky Way.

The Milky Way has somewhere between 100 and 400 billion stars according to Wikipedia (1*10^11 to 4*10^11). A mole of water has 6.022*10^23 molecules in it, each of which has two hydrogen atoms in it for a total of 1.2044*10^24 hydrogen atoms.

10^24 / 10^11 = 10^13 which is ten trillion. So, a mole of water has roughly ten trillion times as many hydrogen atoms as the Milky Way has stars.