Been looking at the 1200XL's video. Atari added a color boost circuit to the 1200 series which makes the burst about half the amplitude of the chroma across the rest of the line. This has the same effect as cranking the Color control on the monitor since the burst defines the reference amplitude. The burst is extraordinarily weak, being about 1/3 of the proper amplitude (@ ~100mV). All other chroma is about 200mV. The chroma is also messy looking. This weak burst means the monitor will increase its internal chroma gain to compensate which causes a lot more color artifacts.
In addition, the sync signal is also very weak so some modern sets won't sync at all and the darker shades of gray probably won't show up. Atari really botched this one, but I do want to experiment with the color boost concept.