I've been experimenting. I put the same info in at Find My Past, Ancestry and Family Search.
Being rather non-specific birth death New York
Ancestry: 1880 Census at #12 1870 at #28 New York Census #32 & 33
Find My: 1880 Census at #15 1870 at #27 1850 at # 25 - 1860 at # 20
Family Search: couldn't find the correct birth year and totally failed in the first 50 responses
I added in the County
Ancestry, 1880, 1870, NY census, NY census, 1850, draft registration, then 1860, all at the top, only one wrong thing in the top eight
Find My: Only came up with the 1840 Census. It didn't find the ones that it found before, even though the four it found before are in the correct county.
Family Search. NY census, NY Census, 3 misses, 1840 census, and a marriage record for their son.