When I was considering my options to upgrade from my Pixel 3 XL, I had landed on the Note 20 as the likely choice (even though the S pen wasn't that big a deal to me)...until the S20 FE specs were announced. I look at the S20 FE as a hybrid of the basic note 20 and the S20, for much less money (usually). I had a chance to buy an S20+ for only $50 more than I got the S20 FE, but still chose the "lesser" FE.
The first thing that comes to mind for a teen is the plastic back on the S20 FE. More durable than the S20's glass back. I also like that it isn't a glossy fingerprint magnet with its more matte finish.
I'm so over curved displays. The S20 siblings have one and the FE has a flat screen.
I figured that the battery would probably last a little bit longer with the FE than any of the other S20 handset. At any rate, I'm happy with battery life after 12 days.
When I want to shoot "important" photos, I use my DSLR, so the phones differing camera arrays aren't a huge deal to me. I do still use the phone camera sometimes, and would like the photos to be good quality, but the level of difficulty isn't going to be too great. If someone only uses their phone for photos, then any differences are probably important. Choose the one that fits the style of photos the person prefers.
I guess it came down to good battery life (that I expected to be better than the more expensive S20s with their higher specs), a flat screen, a matte back that is more durable, and cameras that are very good for the times I need them. The things that would be better for more money weren't worth slightly more money to me, but I'd make the same choice at the same price, too.