What is better for fibromyalgia: cyclobenzaprine or lyrica (pregabalin)?

It depends. Every fibromyalgia patient is different and a medicine that works for one patient may not work for another. Cyclobenzaprine (flexeril) is a muscle relaxant that belongs to a class of drugs called the tricyclic antidepressants. Lyrica (pregabalin) is a seizure medicine that is also used to treat pain. While many patients benefit from these medicines, others don't tolerate them. You will have to try.
Lyrica, (pregabalin) probably. Lyrica (pregabalin), Cymbalta (duloxetine), and savella (milnacipran) are fda approved for fibromyalgia, although other medications including Flexeril (cyclobenzaprine hcl) (cyclobenzaprine) have also been proven to help the symptoms. I am not aware of any studies directly comparing cyclobenzaprine with lyrica, but Lyrica has more data supporting its efficacy than does cyclobenzaprine.