Kathryn- you don't say when you are going but I will assume it is at a time when the snow will not interfere with hiking in the Dolomites. I've been to both the CT and the Dolomites...good news, whichever you choose you will have an awesome time. A couple of things to think about:
Hiking: We stayed in Castleroto (Casleruth) and hiked 3 days there. Lots of hikes to choose from and it was glorious. The hike between the towns is the CT is great and very unique. So this is a push...good hiking in both
Transportation: You don't say how you are traveling around, but if it is by train this could help you make the decision. We had a car, but I got the impression it was harder to get to Castelroto than the CT (which has a train going right down the middle of it) I have a feeling the CT wins this round. If you have a car, it changes. A car can be a hassle in the Cinque Terre since it is better to leave it in Levanto or La Spezia and take the train. I've done that twice and it has always been fine, but not as good as the Dolomites where you can drive it right to your hotel and keep an eye on it.
Uniqueness-Both get high marks here, however the Dolomites will be very different from every where else you are traveling. It really is more like being in Bavaria than Italy.
It's a tough call, I've searched my soul (and memories) and if it were me....Aaaaahhh too hard. I went to both in 2003 and skipped the Dolomites in 2008. You can't go wrong. Pick one and plan on seeing the other your next trip.