I'm so glad you enjoy this design -- I had fun making it!
#13 is a true 2 color.
#7 is really 3 colors and uses screens (shades of one color). B/c of the affordability of full-color digital printing, I would not shy away from a full color logo. The number of colors only drives up the cost in spot color printing. Full color is now more affordable than spot color printing.
That said, It's still smart to have a 2 color and even a single color option of your final design. Those you might want for use on promotional items, embroidery, etc.