Some thoughts from Fort Lauderdale resident
Key Largo
If you are into wrecks and big animals, Key Largo has the upper hand since it simply has more wrecks: Spiegel Grove, Duane, Bibb, Benwood, Eagle, etc. Most of these are in 100 ft and attract Goliath Grouper, Eagle Rays, and some sharks - occasional Reef, Bull, or Hammerhead. The reason I daytrip from Fort Lauderdale is to do the wrecks. But you need advanced certification, and if you are solo you are a bit screwed - pay for a guide. I use Rainbow Reef because they are the only operations that will provide a free guide (tips).
However, Key Lago's reefs are a bit trashed IMO (disease, humans, global warming). Some are quite ugly. And half of Miami is there on the weekends - so it can be quite crowded on popular sites (reefs and wrecks). Frankly, I'd rather spend an hour at the dentist than on the Christ Abyss Statue dive. Be prepared on some shallow reef sites to get kicked in the head by a snorkeler. The State does almost no regulation of diving in the Park - so it's a free for all. But there are still some nice sections of Molasses Reef.
I also do not like Key Largo as a place. US 1 is a giant freeway - almost like being in the exurbs of America (complete with Superstores, fast food, and an Adult Bookstore or two). No beaches. Traffic. A little honky-tonk in parts. Some great fish restaurants, docks, man-made patches of sand, etc. but it really lacks an island vibe. Don't come expecting the Caribbean. The Beach Boys 'Kokomo' song - it's not. But there are watersports galore.
Overall: I like the wrecks, and sea life, but dislike crowds, and layout. I'm in and out and no overnights.
Key West:
Well, there are only 2 major wrecks: Vandenberg and Salvage Master. Newer and I see fewer big fish. The reefs are a lot healthier -especially those in the Sambo preserve. Also, less crowded. Frankly, my favorite reefs in the Keys are off of Big Pine Key - Looe Key/Reef. Why? It's more pristine, less crowded. But I have not been back since Hurricane Irma. Overall, Key West is more of a long weekend dive experience vs. a full week.
Key West as a destination is an American classic. It's San Francisco meets the Caribbean. Lots of things to see and do. Great town with classic bars (The Rum Bar, Green Parrot, Sloppy Joes), restaurants (Blue Heaven), Mallory Square Sunsets, etc. The Lower Keys (Marathon and Onwards) have a real getaway from it all vibe that you don't experience in the Upper Keys. It's not cheap. I will go down for a long weekend every other year or so - it's fun. There are some minor beaches (Fort Henry), but Key West is more about the town, biking, getting out on the water, fishing, diving, sunsets, etc...
Overall
Frankly, if you are thinking of spending one week with a focus on wrecks, I would do both: 3 days in Key Largo, and 2 days in Key West. Something like that. There are even Florida Keys Wreck Treck itineraries.
You need a car if you only doing Key Largo and flying to Key West is kinda pricey. Look at in/out Ft Lauderdale or Miami (FtL might have better car/airfares). And traffic on/off the Keys Fri PM/Sat AM and Sunday returns is quite real.