This is covered in Suppliers to the Confederacy in detail. Some British accourtrement sets were used by Union state troops early in the war, before enough US sets could be produced. I believe these were State of Massachusetts troops in this image from 1861. Overwhelmingly though, Union troops are photographed with US accoutrements. On the CS side, British accoutrements are much more commonly encountered and if period photos are to be trusted most widely used after domestically produced CS accoutrements and captured US accoutrements.