Do you like how the patterned green fabric border looks with the rest of the quilt? For my tastes, it looks a bit busy and it introduces a color (orange, I think), not in the rest of the quilt. If it was my quilt, I would pick a quieter solid or almost-solid fabric for the outer border, probably in gray or darkish turquoise. (If you *do* like how the patterned green fabric looks with the quilt, then ignore all this - it's your quilt and you should do what makes you happy.)
When putting multiple borders on a quilt, the usual approach to have the inner one be narrower and the outer one be wider. Usually this difference is more than 4" and 5.5" borders you are proposing. However, there are no hard fast rules here, and it's your quilt to make the way you choose. Laying things out and then stepping back can help you see what things will look like. Taking a picture while standing up on a chair or step-stool can help you get a more head-on angle to see things better.