I feel it's best to do your buying and trading with your phone carrier, this way you walk in with your old Apple phone get the best deal offered, leave with a brand new phone all set up with all your files photos and contacts in stalled, and you know the phone is working and it's condition.
Also your not sitting at home without a phone waiting for someone at Apple to decide if you will get a trade in and for the phone to arrive.
Myself i don't like the unknown.
But that's not how trade-ins through Apple work at all. I received my two new phones on the 20th (launch day), my trade-in boxes arrived 3 days later, and I had 14 days from then to return the old phones. The return boxes came with a prepaid UPS 2-day priority shipping label from me to them, all I had to do was box the phones up and take them to a UPS location.
I followed the tracking through the UPS app, and Apple notified me that the phones were received on the same day UPS showed delivery. They said they would be evaluated and the trade-ins processed within 72 hours, and both were. Both phones were in the condition I stated on the trade-in appraisal, and I received the full trade-in value on both of them. Apple notified me of that and said the process was completed and there was nothing else I needed to do. The process was flawless, and it was the same 3 years ago when I traded in my last two phones through Apple.
I didn't want to do it through my carrier for a few reasons:
1) There's no guarantee I would have gotten the phone on launch day.
2) I financed the phones through Apple's interest-free financing and got 3% cash back on my Apple Card, which I wouldn't have gotten if going through my carrier.
3) I can pay them off early on my Apple Card (which I will) - if I financed them through the carrier, I'm stuck with that extra payment on my bill for the entire term. Even at 0% interest, I prefer to pay things off and zero out the debt as soon as I can.
4) Depending on the carrier and the store, some of the people working there know less about iPhones than I (or most of us here) do. I want to set my own new phone up, I don't want them touching anything. I'd prefer to do it at home, on my own network at my own pace, and personally see every step of it happening and make every decision about it that needs to be made along the way. And I want to personally wipe my old phone and see with my own eyes that it's done fully and properly, before I hand it over for trade-in.