I have both blender pens and aqua brushes and use both with my dye-based and pigment inks (and watercolor pencils and watercolor crayons). Which brush I grab depends more on the visual result I want for my project and less about the type of ink I'm going to use. I find that the blender pen is great for coloring in small spaces or when you want precise control with where you are coloring. The aqua pen gives me a more "artistic" look and tends to bleed or diffuse more.
With both pens (and ink types) I try to always pick up the color from my ink pad cover and not directly from the pad itself.
Oh, and I find that I can use the blender pen on more paper types than the aqua pen because the aqua pen is more "wet" than the blender pen. But I love both and am glad I have both.