Well, since I am from and live in Panama City, I'll chime in
I guess the difference I see in Panama City and Destin is that Panama City is busy and there is lots to do. Destin seems more of a relaxing vacation whereas PC is active. Just my opinion I guess. They both have beautiful beaches, Destin's are a little whiter. When we had to replentish the beach, Destin pumped the sand from the Gulf of Mexico, where PC shipped theirs in. In PC there are LOTS of minature golf places, the world's largest human maze...do that at night NOT during the day

, bumper boats, clubs..(They have teen nights), Ripley's Believe it or not Museum, a Zoo, Gulf World, the state park, which is great for snorkeling, and Pier Park. And if they are old enough to drive, they will enjoy just cruising the "strip" at night. (Bumper to bumper traffic and teens galore...lol) If you're looking at something close to Pier Park, you won't be disappointed. I love that place. There is a Margaritaville there, which seems to be very popular. And the customary surf shop, Ron Jons. Although if you need a surf shop, I suggest Mr. Surf's on Thomas Drive. My kids get all their surfing and skimming stuff there. Behind most hotels are jet skiing and parasailing. Also banana boats which are UBER FUN! lol. BTW, if you want to parasail look up Adventures at Sea. You can go there and get a parasail ride for 25 bucks where it will cost you 45+ on the beach at a hut. They also have very cool jet ski dolphin tours.
So I guess the question is do you want a place with fewer people, and fewer amenities, or Lots of people and lots of amenities? It's a trade off, and a personal decision, but in reality, PC has more to do for teens.
ETA: As far as the clear water...that's just dependant on the weather and the surf. Some days are clear and beautiful, but some days, like today, the water is kinda murky. Some days there is seaweed, some days jelly fish. I suggest if the water is too rough or too murky to go to the state park. They have a beautiful "lagoon" area surrounded by rocks, which always seems to be beautiful.