Vertical will always be greater than horizontal. The way GNSS works, the calculations that provide the positioning information have a clearer view of the sky to provide horizontal. In fact, while GCPs are great to tie horizontally, they’re really meant to specify the elevation relative to the referenced vertical datum.
If you’re only using GPS (the US GNSS constellation) you’re going to be off by 3-4m horizontally, and 5+ meters vertically. You may see better values for precision, but absolute accuracy will be off.