What an interesting discussion !
To expand on Spectre's expertise, GE conceptualized the doghouse die but it was not in a workable state. Howard Bettner retooled and perfected the die at GE's request,which became a standard in enameling in the 60's and 70's.
The primary goal at that time was to get around the need to thread the wire through solid dies.
From the doghouse (clip die) Howard and his father Carl developed the split dome die which had a more typical approach angle and helped create some hydraulic properties which helped center the wire in the hole, and also maintained the "clip on" appeal of the doghouse die.
As carbide began to be used in enameling dies, threading the dies on the oven became less of a problem because of the longer runs possible before wearing out the dies. However, the split dome die has remained popular for many vertical operations.
As far as the coating quality is concerned, there is not a lot of difference if the dies are used correctly.