What is the reason for this? I understand that the Hobbit was intended as a children's book so elements such as this can be understood, but is there any legitimate reason why these trolls possessed the power of speech and the LOTR trolls didn't that makes logical sense in the narrative?
Because you have many different classes of troll, all with varying levels of sapience.
Stone-trolls were trolls who turned into stone during daylight, like the trolls in The Hobbit. They could speak, and used a debased form of Westron.
Hill-trolls are described in the chronology at one instance as having killed Arador, grandfather of Aragorn. Tolkien described the trolls of that region, including the three from The Hobbit, as stone trolls, suggesting that hill trolls might be a subclass or alternate term for such. However, the Army of the West fought "hill-trolls" of Gorgoroth that could move in sunlight at the Black Gate, implying that these trolls, at least, were Olog-hai rather than stone trolls. All instances of "hill-troll" seem to possess the ability to speak in some form (see stone-troll and olag-hai).
Cave-trolls were seen in Moria, and were also in the Ettenmoors. One was described as having dark greenish scales and black blood. They have a very thick hide. During the fight in Moria, Boromir struck one on the arm and his sword became notched and no damage was done to the Troll.
Mountain-trolls were mentioned once, wielding the great battering ram Grond in shattering the gates of Minas Tirith. From their name, they are generally assumed to live in the mountains, and their choice as the creatures to wield Grond is sometimes taken to suggest that they were particularly strong even for trolls.
Olog-hai were "strong, agile, fierce, and cunning" trolls created by Sauron, not unlike the Uruk-hai, and were able to withstand sunlight while under the sway of Sauron's will. They were also able to speak, but only used the Black Tongue of Mordor.
Half-trolls were troll-like humanoids from Harad who served Sauron in The Battle of the Pelennor Fields. While it is unlikely that they had any actual troll blood in them, it is still possible (but more likely they were a superior breed of orcs and/or men). It is assumed these could also speak.
Disclaimer: The above information is mostly taken from the LOTR Wikia page on Trolls, but enough of my commentary is included that I don't feel comfortable block quoting it.