Tolkien didn't write a ton about the Silvan (or Sindar) Elves; I guess he just didn't find them as interesting as the Noldor. The most I can find about them is from Unfinished Tales, where they're given a brief history and a little more motivation.
The Elves of Mirkwood are very isolationist; they're not very fond of Dwarves (even less so than most other Elves), and they also don't have great relations with the Noldorin Elf-lords (Celeborn, Galadriel, and Gil-galad in particular; emphasis mine):
The Elvish folk of this realm had migrated from the south, being the kin and neighbours of the Elves of Lórien; but they had dwelt in Greenwood the Great east of Anduin. In the Second Age their king, Oropher [the father of Thranduil, father of Legolas], had withdraw northward beyond the Gladden Fields. This he did to be free from the power and encroachments of the Dwarves of Moria, which had grown to be the greatest of the mansions of the Dwarves recorded in history; and also he resented the intrusions of Celeborn and Galadriel into Lórien.
Despite the desire of the Silvan Elves to meddle as little as might be in the affairs of the Noldor and Sindar, or of any other peoples, Dwarves, Men, or Orcs, Oropher had the wisdom to foresee that peace would not return unless Sauron was overcome. He therefore assembled a great army of his now numerous people, and joining with the lesser army of Malgalad of Lórien he led the host of the Silvan Elves to battle. The Silvan Elves were hardy and valiant, but ill-equipped with armour or weapons in comparison with the Eldar of the West; also they were independent, and not disposed to place themselves under the supreme command of Gil-galad. Their losses were thus more grievous than they need have been, even in that terrible war. Malgalad and more than half his following perished in the great battle of the Dagorlad, being cut off from the main host and driven into the Dead Marshes. Oropher was slain in the first assault upon Mordor, rushing forward at the head of his most doughty warriors before Gil-galad had given the signal for the advance. Thranduil his son survived, but when the war ended and Sauron was slain (as it seemed) he led back home barely a third of the army that had marched to war.
Unfinished Tales Part 2: "The Second Age" Appendix B: "The Sindarin Princes of the Silvan Elves"
The general impression is exactly what's given in The Hobbit: they're not bad, they're just nowhere near as mighty or impressive as other Elf kingdoms; Tolkien draws a specific parallel between Thranduil's realm and Doriath, the great Sindarin kingdom of the First Age, and finds it wanting:
He had not the arts nor wealth nor the aid of the Dwarves; and compared with the Elves of Doriath his Silvan folk were rude and rustic. Oropher had come among them with only a handful of Sindar, and they were soon merged with the Silvan Elves, adopting their language and taking names of Silvan form and style.
Unfinished Tales Part 2: "The Second Age" Appendix B: "The Sindarin Princes of the Silvan Elves"
Ultimately, they just want to be left alone:
[T]hey (and other similar adventurers forgotten in the legends or only briefly named) came from Doriath after its ruin and had no desire to leave Middle-earth, nor to be merged with the other Sindar of Beleriand, dominated by the Noldorin Exiles for whom the folk of Doriath had no great love. They wished indeed to become Silvan folk and to return, as they said, to the simple life natural to the Elves before the invitation of the Valar had disturbed it.
Unfinished Tales Part 2: "The Second Age" Appendix B: "The Sindarin Princes of the Silvan Elves"
All of this paints the Silvans in a much more positive light than The Hobbit does, which is a bit understandable; in The Hobbit we're seeing them through the lens of a group they have no interest in even pretending to like. It's not a terribly balanced perspective, all things considered.