Your outernmost ring gets a tile culture per turn equal to your city's cultural output. For each ring outside the tile, the tile gets an extra 20 cpt.
So in a 1cpt city with 100 culture, (so it just expanded borders to its third ring), the third ring tiles get 1cpt, the 2nd ring tiles get 21 cpt, and the first ring tiles get 41 cpt.
What this means in practice is that the important thing is to expand borders first. Unless one city gets two rings "ahead" of the other city, they will typically share the tiles "evenly".
I'm sure there's an article on CFC that explains this more clearly and correctly.
EDIT: So to actually answer your question, no the 1cpt doesn't make a lot of difference as long as your city reaches 100 culture before the other city reaches 500.
EDIT2: Those numbers are for normal speed, on quick speed the third ring is reached at 50 culture and the fourth ring is reached at 250 culture.
I have to run.