Tiffanys since Chanel is costume jewelry. I think at 13, that's the perfect age to get a timeless piece of jewelry. That's when I got mines....although I lost it. But that's not the point, it meant so much to me. At least if they lose it they aren't losing fake expensive jewelry.
i would say tiffany over chanel also. and between the two tiffany pieces, i actually have the first one and i LOVE it! it's the cutest thing in the world and i always get complimented on it. but i'm 24. lol. i think the 2nd tiffany piece would be more appropriate for a 13 yr old.
While it would be refreshing to see a teen in a different jewelry besides tiffanys, I think if you got the 100$ heart pendant, you could as time goes on get another charm, tiffanys or non tiffanys and constantly change up the look by dangling a charm in front of the heart. and you can also engrave her name on it.