Either of those are fine for piecing. I usually piece with a 10 and quilt with a 12, sometimes up to a 14.
But I'm not that fussy either and if all I have are 12s, well I'll piece with them. Wouldn't try quilting with a 10 though...
Edit: I'm big on changing needles. They are cheap in comparison to fabric. Even if it is a new needle if you are having weird problems, change the needle again, it could have a manufacturing defect.
If you ever hear your machine going "pooka pooka" that means your needle is beyond dull and is punching holes in your fabric threads instead of cleverly sneaking in between them.