Pick one to do now and then do the other later. We stayed 3+ days in both places and both are amazing. They are similar, yet different. Both have spectacular ocean views, great scenery, great food, all the hiking you could want, and charming Italian coastal towns.

Cinque Terre - This would possibly require less planning because the 5 coastal towns are connected by a train or by hiking trails. So, you can hike between one and the next, and then take the train for the next. Or, if the weather is good, they also have boats that run from one town to the next so you get another amazing perspective of the towns from the ocean. You could easily have a base and then hike/train wherever you wanted along the coast and return easily wherever you wanted. Can't go wrong going to Cinque Terre

(As others have stated, Pisa and other places are close enough to take a day trip if desired)

Amalfi Coast - There is probably more to see and explore here. We rented a car and I had a blast freaking my wife out as we squeezed between a big bus and the edge of the cliff or the rock wall. Very unique experience driving. You can also take the bus from one place to the next, but when we went the lines for the bus stops were really long so we were glad we had a car. So it would take a little bit of planning to see exactly where you want to drive/take the bus. There is also the island of Capri that is amazing. We took a private boat and it might be one of the greatest things we have ever done on any vacation. BM me for the info. You won't regret it. Pompeii and Naples are close and offer a change of pace. Can't go wrong with the Amalfi Coast.

The Amalfi Coast seemed to have more steep cliffs so walking/hiking was up or down stairs most of the time, where the hikes in Cinque Terre had some steep portions, but it didn't seem as bad. I also might give a slight edge to the Amalfi Coast for food but that just may have been the places we ate. If you go to the Amalfi Coast, get the Bufalla cheese as much as you can. If I had to pick it would depend on what I wanted. If I wanted a somewhat laid back vacation to relax and occasionally go out and hike I would go to Cinque Terre.

If I wanted a little bit more adventure and activity, I'd go to the Amalfi Coast (although you can relax and do hikes in the Amalfi Coast as well, and there are plenty of activities in Cinque Terre). Once you decide and if you have any questions, shoot me a BM