OK, the sun (sort of) came out today. I couldn't get any direct sun photos, but it's decently light out that I feel comfortable with these swatches.
If you have Cooper, you probably don't need the re-release of Pure Pink. They're not 100% the same (especially in formula), but the differences are so slight that it would take an educated eye (ie you know they're different) or to see them side by side in person to catch it.
I know that's slightly out of focus, but it's the only side-by-side for the tubes I got. I was fumbling the lipsticks, camera, and trying desperately to keep my swatches (on the top of my hand)
away from my peach colored coat!
Here's two looks of Cooper and Pure Pink, side by side. Remember, I'm so pale that I'm naturally pink.
I'm not sure if this is as apparent on the monitor as it was to me, but Cooper is slightly warmer (and more opaque with one pass) than Pure Pink. Pure Pink is a cool pink on me, whereas I would call Cooper a warm pink. They're both buildable (multiple passes on both swatches for real color payoff), but I actually prefer the new Pure Pink to Cooper, based on the cool undertones.
Hope this helps!