Well I'll give you my opinion.
First of all, according to the most recent archaeological finds, many of these finds being so recent that they weren't even of public domain when this thread started, the theory which sees the Sherden originating in Sardinia is the most likely, while that of them originating in Sardis or Western Anatolia is supported by nothing.
The name SRDN is attested in Sardinia since at least the 10-8th century bc in the Nora Stone, it is written in phoenician characters.
The Sherden Armor, helmets and swords are found in Southern Corsica, depicted in many stele-statues dating back to 1600 bc, so a long time before the Sherden were mentioned in the Amarna letters for the first time around the 14th century bc.
In Western Anatolia such depictions of helmets or armors were never found, nor before nor after the mention of the Sherden.
The Nuragic warriors of Sardinia are often depicted with horned helmets and circular shields similar to those of the Sherden, some helmets are almost identical to those of the Sherden, plus these depictions are more or less comntemporary to the Sherden, these Nuragic bronze statuettes and stone statues date back to the 12-8th century bc, while the Sherden are mentioned from the 14th to the 8th century bc.
While there are a few Mycenean helmets with horns, such as those depicted in the warrior vase, they're very diffrent from those worn by the Sherden warriors, which have striking similarities to those depicted in Southern Corsica and some of those worn by the Nuragic warriors of Sardinia.
I'll now mention the more recent finds that have occured, many of these in the last few years.
Nuragic potteries dating back to the LBA, the time when the Sherden appeared, used to carry food were found in Sicily, in the Lipari island, in Crete, Mycenean Greece and in Cyprus, this last discovery made in 2010, is especially relevant because Cyprus was attacked by the sea peoples multiples times and the site where the Nuragic pottery has been found was considered a sea people site, this discovery has caused archeologists to rethink the origin of the Sherden, possibly being "refugees" or merchants/sailors from Sardinia.
A really recent analysis of these bronze ingots revealed that many of them came from the red sea and the Sinai Peninsula, which was under the control of Egypt at the time, which reincorces the theory which sees the Nuragic Sardinians as the Sherden who were present in Egypt as mercenaries and royal guards of the pharaoh.
Remember that Sardinia had a special relationship with Cyprus and the Eastern Mediterranean during the bronze age compared to the rest of the Western mediterranean including the rest of Italy, the greatest amount of oxhide bronze ingots in the Mediterranean was found in Sardinia, more bronze ingot were found in Sardinia than in Crete or Cyprus itself.
Furthermore the connection between Sardinia and the Eastern Mediterranean is reinforced by the recent finds of melon seeds in Nuragic well dating back to 1350-1120 bc, at the time these seeds were grown only in Egypt and the Near East.
An argument that I've seen in this thread against the identification between the Sardinians and the Sherden is that Sardinia did
not have the technology at the time to produce bronze weapons, this is competely false.
Copper swords were present in Sardinia since 1600 bc, see the Sant'Iroxi swords for instance, these are among the earliest swords found in Europe, furthermore bronze daggers spears and axes are found in the island since the medium bronze age, and votive bronze swords were present in burials and temples dated to the XIV-XIIIth century bc, these finds testify the importance of swords in the Nuragic society, so yes, bronze weapons were a thing in Sardinia during the time period of the Sherden, and the Nuragic daggers have interesting parallels to those used by the Sherden and found in the Levant.
Another interesting note, a recent study (2013) has proved that over 60% of the copper used in bronze swords in Scandinavia was from Sardinia, and we're talkking about a period around 1500 bc, to give you an idea of how Sardinia held a huge place in the trade netwrok of the Bronze age.
I think I gave you a good amount of reasons to consider why the Sherden most likely originated from Sardinia and later migrated to the East, rather than the countrary.
Now I'll tell you why I don't believe that the Sherden originated from Sardis or Western Anatolia:
1)The Sherden were really numerous according to the Egyptian records, and they were highly regarded as sailors and warriors by them, then if they came from Western Anatolia, why are they never mentioned by the Hittities, despite the Hittites mentioning other Western Anatolians people and their lands multiples times, such as the Carians and the Licians, who were known by the same name to the Egyptians?
Why, despite the Hittities mentioning cities as far west as the Western Coast of Anatolia multiple times :Miletus, Ephesus, Wilusa (Troy), they never mention the Sherden or the city of Sardis?
The Hittities even mention the Myceneans/Acheans, who lived in Greece, why not the Sherden, who were much closer to their homeland, why did they mention the Carians, and not the Sherden, who were much more highly regarded by the Egyptians, being taken as royal guards?
2)Where is the archeological evidence for the people of Sardis being the Sherden?
According to the few depiction of Lydian and Western Anatolia warriors, they all look extremely different from the Sherden, why is that?
Also in Sardinia we have bronze age scarabs dated to the time of Ramsess the second, such as that found in the necropolis of Monte Prama, where the bones were dated to 1100-900 bc too, why are there no such finds in Sardis? Also Sardinia had a huge "industry" of Egyptian scarabs during the early iron age, so huge that Sardinia has the highest number of Scarabs in the Mediterranean, it's only next to Palestine and Egypt itself.
Scarabs had an important meaning in Sardinian society, while in the Western Anatolian one they had none, this makes no sense if the Sherden came from Anatolia, but it makes a lot of sense if the Sherden were Sardinians.
3)The Egyptian records do speak of the origins of the Sherden, according to the Egyptians they came from the midst of the sea, with their warships, no one being able to withstand them.
So their homeland is in the midst of the sea, this sounds like an island to me (Sardinia), not like Sardis, which is an inland city 150 km away from the coast, it makes absolutely no sense for a people known for their skill as sailor to come from a city far way from the coast.