LOVE this question!!! It is personal choice in the end, so this is just my opinion. My first thought.... SILVER!! I love silver!! A really easy thing to do with very little cost. By painting the portion (you can not remove) you would give an illusion of a seperat small area! Actually any contrasting color would give it a nice appearence, I like silver. I would make sure to paint the inside walls and underside the same contrasting color. If you go for everything all the same I would at least get a little crazy and paint the area with a top coat of clear-glow in the dark :) (kiddin)

I've always felt that painting the ceiling colour on the underside of the bulkhead not only appears to lower the ceiling, the room seems more chopped up. Here's a link -- it seems to be the consensus, online, to paint the entire bulkhead the same as the wall:

http://therenoprojects.blogspot.ca/2014/04/design-dilemma-painting-bulkheads.html

Thank you all so much for the feedback! It is exactly the info I was looking for and will be painting the full soffit, both front and underside, later today. Much appreciated!!!

i'd paint the facing portion of it in the wall color, and the ceiling of it white. i hope that makes sense.

I live the idwa of wall color continuing across soffit but would appreciate input where Soviet also continues into small hallway (about 8') before reaching a clean separation to new room and vaulted ceilings. Would small hallway space close in with walks and ceiling same color? No recessed accent at this point like kitchen

I would paint walls, soffit and ceiling all the same color so that the eye will flow. Another option is if you have white cabinets, paint the soffit the same color as cabinets so that the eye flows upwards instead of stopping