I would prefer the stain. Since you have paint splotches all over the house, you cant use a regular type stain, it will have to be solid color. Unfortunately solid color stain, is very much like paint, and yes, it can and will peel like paint will. What it appears you have on your house now, is an oil based semi transparant stain in a darker gray. That would have been what I would have chosen to re do. With all the pain splotches, that is no longer an option. Since it sounds like you are also changing the color, I would go with the solid color stain.
Q