In the end, it all comes down to luck.
The game doesn't say we have different odds at 1 and 10+1, so all we can do is experiment on our own.
From my experience, I've had some 6* girls from single pulls, both on DMM and Nutaku and for a while I stayed away from 10+1, but hit a dry streak.
After doing a few 10+1 then, I had other rainbows, so I think it's a matter of chance.
In conclusion, I think 10+1 is better because of the extra pull and the Rainbow Shards mentioned by maotd.
Name: Volarmis
DMM ID: 317568967