19" arcade monitor is more like a 21" computer monitor. Arcade monitors are measured horizontal width (though lot's of times, it seems as if they include their mounting brackets in the measurement for framing purposes) and computer monitors/tvs are measured diagonally.
Actually. Arcade monitors use the same tubes as televisions, and I believe there are laws about TV tube advertised size, vs actual size (laws which don't apply to computer monitors), which is why a 19" TV or 19" arcade monitor is always bigger than a 19" computer monitor.
Also, every 19" arcade monitor I have ever seen had the exact same sized tube, regardless of mounting schemes.
As to which monitor to put in the cabinet? Eh, might as well use the 15", you are already going with an X-Arcade, so the thing isn't going to look right anyway.