The Mills definitely allow more information through, so it's a worthwhile upgrade.
The only downside I find upgrading cement or even metal oxide to Mills is the additional information Mills provides can be a little distracting, it almost sounds louder, so I usually choose the next highest size Mills over what I'm replacing to restore the musical balance. Thankfully, they come in small increments so it is easy to fine tune. From what I see there is 4.0, 4.2, 4.3, 4.5 so you're covered! You're fine to bump the 3.9 to 4.0, the difference is probably too small to notice. I would also buy the next biggest size 4.2? to try in comparison. Just clip them in while testing so you can return whichever you don't like.
Try red Jantzen Superior-Z for the caps, if they will fit. Great value, imo.