In my opinion, your best bet for a NARS lip color similar to "Brownie Nude" would be NARS Lipstick in "Mindgame" or even "Hot Voodoo". Colorwise these products are almost exact replicas of Bobbi Brown's "Brownie Nude" though I'm not sure how it compares in other departments. To my understanding, NARS lipsticks deliver highly pigmented, ultra-matte color, and can be a tad bit drying. So as far as formulas go B.B.'s Treatment Lip Shine and NARS lipsticks are not quite the same.
Here's some pictures of the two colors:
Mindgame Hot Voodoo
As far as Sephora lip colors go, I would say Lip Additude-Star in "Fabulous Brown" is the closest in hue to "Brownie Nude." Unlike the NARS lipsticks, Lip Attitude-Star provides a subtler color that combines the "perfect amount of lipstick and lipgloss," much like that of the Treatment Lip Shine.
Hope this helps!
Hi! Out of the Nars lipsticks, the two with a pretty close description to the Bobbi Brown lipstick you liked were the Nars shades Mindgame and Tanganyka. The Bobbi brown lipstick is more pinkish plumish than Mindgame though, and is closer to Tanganyka, so I would go with that. You might want to test it out in the store to make sure it's what you are looking for.