In my personal experience, the woven nylon band 'breathes' better, and doesn't feel as sticky on the skin as the rubber band. Definitely a step up in comfort. Plus, the nylon band is quite light in comparison, which makes the aluminium watch feel super light overall as well. Other than the tactile feel of it being there, one almost can't tell it's being worn at all.
On the other hand, the woven nylon band also absorbs sweat and skin crud and needs more intense cleaning compared to rubber to avoid discoloration. I occasionally let my band soak in a small container of warm water with some detergent for a while, then I rinse it off and let dry. Good as new, almost.
The band also wears (or 'acquires a patina') slightly more readily than the rubber band, but it's nothing to be concerned about really. I've had my band for like a year and a half or so now, it's held up quite well.
The woven sport loop should feel even lighter and breathe even better due to its fuzzy nature. I've only tested it on quite briefly so I can't tell much of the experience, but it felt nice. Hopefully the velcro fastening strips don't become loose with use.