Legolas was one of the Sindar, a member of the Third Clan of the Elves who were abandoned while searching for Thingol (or otherwise left behind) right at the end of the Great March. Legolas himself probably doesn't date back that far, but his ancestry is in the ancient Sindarin kingdom of Doriath (his grandfather was Oropher, an Elf of Doriath, who must have been of reasonably high birth, being accepted as king of the Silvan Elves of the Greenwood in the Second Age).
By standards of Elves left behind in Middle Earth, he's reasonably exceptional, if a little rustic (as a result of the predominantly Silvan culture he lives in), finding the Noldor (High Elves of Middle Earth) strange but still able to read their past in the renamnts of their work:
'The Elves of this land were of a race strange to us of the Silvan folk, and the trees and the grass do not now remember them; only I hear the stones lament them: deep they delved us, fair they wrought us, high they builded us; but they are gone. They are gone. They sought the Havens long ago.'
(Source: The Ring Goes South)
Roughly half of all the Elves refused to go on the Great March, and of those that did go, a sizable enough portion of the Third Clan turned aside at the Misty Mountains. That puts him as once of a still significant proportion who (or who's ancestors) made it to Beleriand. As a member of the Clan of the Teleri, he can be expected to share characteristics of that folk:
All Telerin peoples, from Valinor to the Silvan Elves, share a love for music and song and for water. While the Noldor built great cities, the Teleri lived in simple dwellings such as the 'flets' of Doriath and Lothlorien ... The Teleri have a strong connection to nature and its cycles and have far less interest in the Valar than the Noldor and Vanyar, preferring the company of their own people and other Elven cultures ... The Teleri value silver more than gold and have a love for pearls, boats and shorebirds such as swans.
So for a member of the Third Clan he's quite high-ranking in Middle Earth, but the Teleri of Valinor (being also High Elves) would be counted as more exceptional. There are others in Middle Earth who would completely outclass him, however.
Galadriel is the most obvious; she's a Noldo originally from Valinor and has been ranked by Tolkien as - together with Feanor - one of the mightiest of the Eldar of Valinor (can't quite recall the source; may be History of Galadriel and Celeborn).
Celeborn was a kinsman of Thingol, which puts him extremely high up the pecking order of the remaining Sindar.
Glorfindel was also a Noldo of Valinor, fought in the Fall of Gondolin, was restored to life and sent back to aid in the fight against Sauron (source: "Glorfindel" essay in HoME 12).
Elrond was the last remaining heir of Finwe in Middle Earth (...barring one interesting case...), original High King of the Noldor in Valinor, and is of mixed Noldor/Vanyar/Teleri/Human/Maiar descent.
Maglor, a son of Feanor, may still be alive in the Third Age, and was renowned as the mightiest singer of the Eldar.
Cirdan, another Sindarin Elf, was probably the oldest Elf remaining in Middle Earth and may even date back to Cuiviénen; he's well-attested to have seen deeper and further than any in Middle Earth.
These examples may seem long-winded and belabouring a point, but they are the truly exceptional Elves at the end of the Third Age. The head honchos of Elvendom, if you will. Legolas as a son of a relatively minor family (by these standards) in a backwater/rustic kingdom would be several notches below them in the "exceptional" stakes, but still several notches above the Silvan/Avarin Elves which would be the norm for Middle Earth at that time.
Not sure how well that satisfies your question, but it should give you a good idea of where Legolas fits in Elf terms.
(All uncited sources: The Silmarillion and Quendi and Eldar)