Almalfia Coast or Cinque Terra

It's Amalfi.

It depends on how many nights you want to spend in either. The Amalfi coast/Gulf of Naples area with all the things around there (Capri, Positano, Amalfi, Naples, Pompeii, etc.) needs at least 4 or 5 nights at the very bare minimum. The Cinque Terre doesn't have as much to see and do, so it can be covered easily with a full day (basically a couple of nights).

You could do either, but with 14 days (does that mean 13 nights?), Cinque Terre would be better logistically. Less travelling back and forth.

BTW, it is Cinque Terre and Amalfi Coast :)

Yes, I had a feeling I spelled incorrectly... I was on my phone!!

What the 2 posters above me said.

If you have at minimum 4 nights to give, Amalfi Coast
I think it is more impressive for shear beauty, it is a much larger area though, with much more to see and do and definitely requires more time.
If you have 2 or 3 nights max, stick with Cinque Terre.
Given the locations you also want to see it seems the Cinque Terre will probably fit into the plans better.

joan,

The Amalfi Coast and the Cinque Terre are each somewhat unique, so it's difficult to make a comparison between them. The resort towns on the Amalfi Coast tend to be more "formal & posh" while the Cinque Terre tends to be more "informal and rustic" (at least IMO). I agree with the others in that you'll need to allocate at least four days for the Amalfi Coast.

Given the other locations you're visiting, the Cinque Terre would be the easiest location to fit into the plans, especially if you follow the route Venice > Florence > Cinque Terre > Rome. All locations are well served by rail, so transportation will be very easy. OTOH, transportation along the Amalfi Coast is a bit more challenging in some cases. Sorrento is served by rail service (as well as bus and boat), although the train is the somewhat "colourful" Circumvesuviana, which has a bit of a reputation as a haven for pickpockets and scammers. Positano has only bus, boat and road access.

You'll see the "beauty and wonder of the coast" in either location, but the view will be a bit different in each case - not better or worse, just different.

We had to make the same choice and wound up going with CT, based upon the overwhelming response from friends (but we will see Amalfi at some point!). I agree with the others that the logistics work better for CT, so you don't have to back track from Amalfi back up to Rome or Naples (if it's your last stop). On the train, we took it from Venice to CT (you can go south and switch in Florence or north and switch in Milan) and then stopped in Pisa for a few hours on our way back to Florence to see the Tower (checked our bags at the train station).

Just returned from a too-brief stop in Minori, on the Amalfi Coast. Even in July, it is laid back and not heavily touristed. Nothing posh about it.

I love the Amalfi Coast so that's my bias. I spent less than a day in Monterosso and felt like an anchovy.

Both are stunningly beautiful! IMHO, it depends how active you want your experience. If you choose Cinque Terra, you are able to take a day hiking the coastal path through all five towns (or less if you desire). The path can be rather challenging, but well worth it.