The stock JB with a UOA5 mag swap is a thing of beauty. Smooths it right out, adds clarity and retains nice mids.
Both of the pickups you inquired about are great for what you're after.
Personally, I like the AT-1 I have a lot, though I de-aired it (got rid of the plastic spacers that hold the magnet away from the poles and put in a metal spacer [trimmed allen key] so everything makes contact)