Growing up, I feel like I had the experience of being both--but not at the same time.
When I was a kid, probably up until I was 11 or 12, I was constantly told, "You are going to grow up to be gorgeous"--among other various compliments about how pretty, exotic, adorable I was. Almost every day, friends, family, teachers would bring up something positive about my appearance---it sounds ridiculous, and it was, but that constant positive affirmation of being really pretty burned itself into my brain. Even strangers would stop my mom and I on the street to comment on how how beautiful I would grow up to be. The message that I really took from all of that was, 'hey, being beautiful is a really important part of who I am'.
When puberty hit, I stopped hearing frequent compliments very suddenly, and it really threw me for a loop....am I not beautiful anymore? Are people disappointed that I'm not becoming as pretty as they thought I would be? It felt like I had failed, somehow. It was a strange identity crisis for essentially a child to be having---but that's what happens, I guess, when the world goes from showering you with compliments every day to only a few compliments here and there. I convinced myself that the compliments I still got were because people felt bad for me.
I'd always done well in school, but at this point I dove headlong into my coursework and was consistently at the top of my class. I started to dress in baggy, unflattering clothes, and to wear my hair over my face to detract even more attention from how I looked, because I convinced myself that I must be hideous, now, since no one was telling me otherwise. Which is...yeah. That's where my head was. It probably didn't help matters that my family moved around a lot, and so in addition to dealing with my own clear self-esteem issues, I was constantly the 'new kid'---and my perpetual experience as an outsider only reinforced my feeling that I was unlikable, undesirable, and what not. I was not a popular teenager. But I was a "smart girl". That's one of the only things that people ever noticed me for from age 13-17.
And hard work in school made me valedictorian and got me perfect SAT and near-perfect ACT scores. I had a broad pick of really excellent universities, though I didn't get into my top choice, which was a blow to my hard-forged 'smart girl' identity, because, wait...does this mean I'm not smart either?!
Then, in college, I was suddenly "pretty" again, which fucked with my brain even more. The compliments started to return, and it made me feel really good---as much as I hated how much power this "pretty" thing had over me. In a weird way, it took me right back to childhood---all of this positive reinforcement tapped into that child-like desire for approval----so to keep it coming, I started dressing in a more flattering way, brushing my hair, putting on makeup to highlight my best features. And the response was overwhelmingly positive. I started getting a metric fuck ton of male attention all at once, and I was completely unprepared and unsure how to deal with it (having had little experience). Looking back, I'm ashamed to admit my college grades did suffer...instead of studying, I was dating, going out constantly, reveling in the feeling that I had finally lived up to peoples' expectations that I would grow up to be a good-looking adult, ingrained all those years ago. It's messed up and I feel stupid saying it, but I really did feel that way.
I graduated with decent enough grades, but nothing stellar. I went on to get my masters, and am considering a PhD--reportedly I'm pretty smart. People still regularly compliment me on my appearance, and I think I look nice. But I'd also like to think that feeling really smart and feeling really pretty doesn't impact my self-worth as much as it used to--- but of course it still impacts my thinking from time to time.
I think the best thing to ingrain into children is that they are good hearted (most children are) and that they should strive to be good, kind people---because that's one of the healthiest things to cultivate selfhood around, I think. And I think it's worth making an effort to teach kids and young adults to not rely so much on outside validation to feel good---because that's really at the crux of the whole "pretty/smart" girl issue. Girls who are smart want to be seen by others as pretty; girls who are pretty want to be seen by others as smart....so really a big part of it is just teaching people to to be happy in their own skin.
Easier said than done, obviously, but it's what I would have wished for a younger-me.