A lot of the change is due to the character arc Spock went through in TMP. When he first arrives on the Enterprise his voice is cold and flat. Later, after his flight through V'Ger, his voice warms up, and he begins to sound like the Spock of old.
There was an aging factor because his voice was deeper and growlier in general by the time of TMP, but it's also true there was a character-driven harshness to it in TMP when he first arrived on the Enterprise versus after the encounter with V'ger. Contrast "Twelfth power energy field" with "Yes, Captain, we witnessed a birth."
Actually, if you listen closely, Spock's voice in TMP is mostly "cold and flat" in the bridge scenes, and more expressive in scenes on other sets such as the officer's lounge. Keep in mind that all the bridge dialogue was looped (dubbed over) in post-production due to the noise of the film projectors behind the bridge consoles. Evidently Nimoy just gave a stiffer performance on the dubbing stage than he did on the set.
It's true that he was more expressive in later bridge scenes, but he also was in the earlier lounge scene. And there is a noticeable difference in the timbre of his voice in all the bridge scenes versus scenes elsewhere.