Outline stitch vs stitch in ditch
 

Do I stitch on both sides of the seam?

I wouldn't.

I'm assuming that by outline you mean sew about 1/8 to 1/4" away from the seam.
As long as the batting requirements are met, it's a matter of personal preference. I let the piecing be my guide as to what I want to highlight. Sometimes I sew on both sides, sometimes on just one side.

Wish you had posted a photo. You usually don't have to do both so look at the quilt and see what might look best for the quilt top. Usually the outline stitch is done around applique but there are no rules.

I don't sew on both sides. It is so much faster to just sew beside the seam and not "in the ditch". On one side. Here's one...I did.

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I wish you specified if you are machine quilting or hand quilting. If by machine, it all depends on the look you are going for. sometimes when you outline (assuming you are talking 1/4" to the side of the seam) on both sides, without ditching as well, it makes the area where the seam is poof up. But when hand quilting this effect is not quite as obvious. When hand quilting I usually outlined on both sides of the seam and never ditched. I liked the look of that. But it really boils down to what you want it to look like and if you are fulfilling your batting's minimum quilting requirements.

I always check the batting requirements and go from there.

I prefer to sew like the above picture. Very hard to stay in the ditch.

I like the way justflyingin did it. The stitching gives the quilting a great look.

I like to stitch on both sides of the seam. It takes a bit longer, but I like it. I agree with others though that it is a matter of preference.