This would no longer be a formula date field but a formula text field. Anything with color, not using script, would be text. Someone else here can probably provide you the jquery or js to do that. But here is out of the box QB using formula text.
"<div style='color:#FF0000'>" & [Date Complete]-[Start] & "</div>",
"<div style='color:#0000FF'>" & Today() - [Start] & "<div>"
Try this and see if you get the results you want. Notice the single quotes around the color styles. Again, you have to set the data type to formula text and turn on "allow html".
Hope this helps.