Since it's a scarf and the size is not critical, you can use either of your needles. On the 10 it will be smaller, and on the 13 it will be larger. If it's a plain scarf you can just decrease the number of stitches you cast on. If it's a pattern that can't be easily changed--decide what you'd rather have--bigger or smaller.
"Trust the pattern!"
Time flies like an arrow, but fruit flies like a banana.
Hop aboard while we follow the cloud-covered van of knitting harmony, man!! Woooo!! --Hedgehog
IngridKH on Ravelry