I really like both. Like the sport for wonderful feel and ease of cleaning. I like the woven for it's airiness on the wrist, and the pattern is a really unique look.
I did vote for the Woven but depending on where you wear it, I suspect anything with a non-solid surface will eventually trap dirt, etc. within the weave. Just like I suspect the Milanese will too. Worse would be getting dirt or mud I suppose or an oil or gooey substance. The woven is spot clean only, whereas the sport can be run under water, Magic Erasered for stains. So they both have their place on a wrist.