Early LP's themselves are often remarkably different than later ones, in general or by specific Player, due to changing tastes and expectations and overuse or disinterest in some ideas. As well, youtube's former 10/15 minute timelimit forced many videos hosted there to be awkwardly cut from the original long session into bits, often abruptly.
Certain Let's Plays can change format, pacing, and even tone. Take, for example, seiferguy's LP of Zelda II: The Adventure of Link. The stark contrast between the first and last chapters must be seen to be believed.
In Nakar's playthrough of Ultima VII Part II: Serpent Isle, Steve the Avatar appears utterly oblivious to the concept of sex, even as the sorceress Frigidazzi is openly trying to seduce her, kiss her, and strip before her. Two games prior, she paid a gypsy lady to have sex with a mouse while she watched. On the other hand, being an utter sociopath has been a firmly established trait since the beginning.
raocow's earlier vids had him sounding dull and tired, with nary a joke in sight. Over time, he evolved into the very idiosyncratic Talkative Loon we've come to love.
He also had a much thicker accent in the early days; in fact, on some of his earliest videos (on Dailymotion instead of Youtube), he can be pretty hard to understand at times, often lapsing back into French. Eventually, he developed a higher-pitched, wackier voice with almost no trace of an accent.
PewDiePie's original talkthrough of "Amnesia The Dark Descent" lacks most of his trademark quirks. Most notably, in the first video he says that he hasn't played a lot of horror games. He also actually collects the tinderboxes, is a lot more scared, has a thicker accent, and isn't constantly yelling. At one point he throws Stephano and runs. Perhaps his most jarring difference is that he doesn't have his rivalry with the "BARRELS!" The Alien Abduction custom story is when he becomes the persona that is either loved or hated by so many for what tend to be the exact same reasons.
Sir Ron Lionheart may be the ultimate example of this trope. Go listen to episode I of his Let's Play of Super Mario 64(-bit), then, say, episode XX, and finally, try episode CXXII and observe the evolution of a legend. OH WHAT THE-! YEAH! FANTASTIC!
Their first video, Two Best Friends Play Kirby's Epic Yarn, which was recorded via camera pointed at the television instead of a video capture device. Their personalities are also radically different, with Pat behaving far more goofishly and Matt being the straight man, with little-to-no gags or humour in favour of just them straightforward bickering at one another.
The first two or so seasons of their machinima series also plays up their routines (Pat as the angry, abusive one and Matt as the dumb, childish, goofish one) far more. They would also feign ignorance on numerous subjects, the most obvious examples being in their Marvel vs. Capcom 3 video. It's jarring to watch their full-lengthed LP's and later Machinima episodes, where they act far more naturally and display a thorough knowledge of video games and the industry, then go back to their Resident Evil 4 episode and watch Matt obliviously and ignorantly dismissing the game as bad for trivial reasons and Pat going into sputtering rages over each and everything he does.
Roahm Mythril actually addresses this trope as "First Game Syndrome".
Ant Dude 92's Let's Plays on his original channel, Sonik Dude 101 (which is still active, with a large number of his old videos still present) were very different in tone to his newer Let's Plays on his current channel.
His original personality was more sardonic, as he often criticized or made dark jokes about certain game elements (for example, suggesting that Spyro character Hunter is a rapist in Spyro 2: Ripto's Rage). He often used harsher language when getting frustrated, sometimes screaming in anger, and had less of a connection with his audience. Also, the video quality of his older videos were poorer than the high-definition, well-edited Let's Plays he uploads now.
Nowadays, he has an upbeat, welcoming, family-friendly personality, very rarely swears or gets frustrated (instead seeing the humour in failure), and rarely makes criticisms towards the games he plays. His videos now have brighter colours, intros and outros, and have numbered video thumbnails. Lastly, he reviews games, both new and old, more often.
Also, when his channel opened in 2011, he disguised his voice slightly in an attempt reinvent his identity. Over time however, his old fans realised who it was, so he reverted to his original voice.