The best thing to do with the text beneath the banner is to give it the SAME text color and the same ghostly border as the primary text. One of the rules of banner design is not to allow too many types of contrast or the image looks "broken"... like too many parts instead of multiple elements of one single part, ya know?
Because the text is smaller and wider, it has its own emphasis, but still, it's only one change - dimension. By making the text green with a red border, you're not "killing it with contrast", as I call it. You're changing one thing - dimension. Everything else is uniform and thus looks like an element rather than its own separate part.
The example provided by krrc is another example of killing it with contrast, but not because of the colors used - this actually gives it more uniform because it uses the same colors as the primary logo. (Good choice on that one, krrc). However, the pattern itself is too busy, so it kills with contrast. A more steady line would look fabulous in the example provided.
But, this is just my opinion. I've been doing graphic design for a long time, and there are some rules I've found that work for me. Other artists and viewers may have a different perspective.