Both archaeological sites are worth a daily visit, but Akrotiri is the most important one because it provides unparalleled view and understanding of Bronze Age people in the Aegean.
The Archaeological site at the location Akrotiri encloses the excavations of a Bronze age town that was buried under volcanic material sometime between 1627 and 1600 BCE. It is similar to the better promoted Pompeii, but it's worth noting that Akrotiri predates the Italian town by about 1600 years! The volcanic ash that buried Akrotiri also preserved it in pristine condition for us to enjoy. The fact that no casualties or portable valuables indicates that the island's inhabitants probably had ample warning and fled before the volcano exploded.
But their homes remained as a silent witness to a joyous and affluent life. The best known artifacts from Akrotiri are the exquisite wall frescoes that decorated the prehistoric buildings. The best frescoes are on view at the Archaeological Museum of Athens, but many, just as beautiful can be found at the Museum of Prehistoric Art in Santorini. The excavated city of Akrotiri and it's artifacts are rare and very valuable for our understanding of life in the Bronze Age Greece.
Even though the archaeological site called "Ancient Thera" or "Ancient Santorini" cannot match Akrotiri's historical importance and uniqueness, it offers evidence of Hellenistic, Roman, and Byzantine cultures through the ruins exposed on the barren rock they call Mesa Vouno on the South shore of the island.
To put things in perspective, Ancient Thera's ruins represent an time between 500 and 2000 years after Akrotiri was buried in volcanic ashes. And by that time Thera island was not considered an important center of Ancient Greek civilization. it was by no means insignificant, but other centers dominated Archaic, Classical, and Hellenistic eras (Delos, Paros, Naxos, Rhodes, Kos, and Crete were all more important cultural and economic hubs of that era)
But what it lacks in archaeological prowess, Ancient Thera makes up with spectacular views of the island and the Aegean. It's ruins occupy the highest (and geologically the most ancient) mount on the island, and the Aegean sea itself betrays its importance as it provides the dramatic blue backdrop for the excavated ruins. The little theatre on the site is very picturesque, and invites the visitors to imagine how beautiful the plays must have been for ancient Greeks who watched them against such a dramatic, deep blue background.
The artifacts from Akrotiri are housed in the Museum of Prehistoric Art in the town of Fira. It's a large museum, unique in its scope, and well worth a visit. It houses exquisite frescoes, art, and every day objects, as well as thematic entities that shed light on the island, it's people and their lives in the Bronze Age. It also has a several displays that shed light in the island's connections and commercial ties to other Greek centers around the Aegean, with Egypt, and the Levant. You can browse it's exhibits comfortably within half hour.
The "Ancient Thera" museum is much smaller, and the artifacts date from the Archaic, Classical, Hellenistic/Roman eras, most of which were unearthed in the Ancient Thera site. It's a tiny provincial museum, so you can comfortably browse it's halls in about twenty minutes.
The third attraction of the island, is the Thera Foundation, also in Fira town. It's not an archaeological site, nor a museum, but a display of three dimensional reproductions of wall paintings from Akrotiri. High resolution paintings adorn interior room reproductions to give visitors an idea how the interiors of the buildings felt with the wall frescoes. It's a complement to visiting Akrotiri (where the interiors of homes are off limits) but not a substitute for it. As such it's worth a visit for anyone who is interested in gaining a better understanding of Bronze Age life and culture.
Read more about the history of Santorini ...