Copied from OP's comment:
I believe he stayed in the Aachen area.
It is a photo of my G.G.Grandfather who was born in Aachen, Germany in 1841 and died 13 Nov 1890. Thanks in advance.
As this map of Germany between 1815 and 1866, Aachen was part of the Kingdom of Prussia. (Aachen is just inside the border with the Netherlands, roughly just West from Köln.)
If your Great Great Grandfather remained in Aachen it is almost certain that the uniform would be Prussian. Your G.G. Grandfather's uniform looks to be a Waffenrock, the uniform adopted for most Prussian uniforms from 1842 until early in the 20th century.