I love the beach, and I love the cliffs BUT....as a solo traveller, the beach wins out. Its just easier to get out and mingle if you feel like it. I also prefer walking the beach to the side of the cliff road (done that and didnt like it one bit). Early morning walk is essential in JA to counteract all the good food going down!
If you want complete privacy, peace and quiet, then the cliffs fit the bill.
Perfect trip: at least 2 weeks, with a few days on the cliffs to start (unwind, relax, nap, eat) then hit the beach for the rest.

PS...I agree with Maryanne...waves crashing on the cliffs when you are solo can get you thinking....sigh...alone again....sigh....lolol