i think in a way the most clear characterisation difference that has emerged between book!lestat and show!lestat is in the character's relationship with agency (both how he does or does not display it, as well at what it represents for him).
book!lestat is in many ways characterised by his (to a surprisingly high although definitely not complete degree) taking responsibility for the things he does, as well as his reframing of things he did not want as things he DID want. i will cite as clear examples for the former the turning of david talbot (he feels wretched about it later but he does it himself and admits to it As being an awful thing to do) and the turning of claudia (he wants her, and despite his later grief and guilt he says he would do it again). for the latter i will cite his total acceptance and embracing of vampirism (<- something done so he can avoid acknowledging that his turning was a violation) and (though this is partly in the first category as well) his guilt for the actions he takes when under akasha's control and dependent on her blood. (there is a particularly chilling passage involving the "killing gift" (exploding people with mind) and lestat purposefully covering his hands in the blood of his victims to tell himself that he brought on this carnage, no matter if under orders). even in the shrine with akasha, he apologises to marius for waking her and enkil though he didn't know it would happen and he very much seemed coerced (pulled along etc) to do it.
in contrast to these particular examples, show!lestat has to be persuaded into turning claudia (something that works out interestingly so that's not one i take that much issue with) and wants to avoid feeling any guilt for what happened to her and his (much more active than book!lestat, mind you) role in it (<- see how long stained glass eyes takes to come out). david talbot is a moot point. the embracing of vampirism is similar in that it is required for the plot, but the very clear reframing of it as shown in tvl '85 (scene where lestat, looking into a mirror and trying not to cry at not being able to recognise himself, smiles at his transformed visage and finds his old self in it (one of the most eerie and beautifully written scenes in that book. to me. and it happens not long after the passage where he refuses the blood over and over!!), his first few nights in vampirism) is largely absent. akasha's (potential) role in his actions illustrates the difference most clearly. in speaking about the impact of her blood on him (end of 3x05), he describes the experience with imagery showing he cannot control its effects, and that actions taken under it are not his (he starts by saying he can "unleash" the "hell" of the blood ("metal sun" in "veins" almost certainly refers to the blood itself), but goes on to say that the blood "cannot be restrained in the moment or tamed over time" and that "it drags you [the hypothetical, but 1x05 (!!) flashbacks over narration show he counts himself in it] into depravity".
really, the difference is illustrated in plot elements as well. book!lestat: goes out to kill the wolves by his own volition like he has something to prove, joins satan's night out on his own and keeps his music career (ephemeral as it is) going under his own steam for his own motives, finds a job at the theatre on his own, seeks marius out on his own, semi-mutually leaves gabrielle (post the conversation about the letters) on his own, SITS DOWN TO TELL (write down!! very important if illiteracy element had been kept!!!!) HIS STORY OF HIS OWN WILL, ON HIS OWN (<- perhaps the most significant application of this idea). he wants to find/make meaning for his life in an existence he has long ago found to be meaningless, and his story as something that has meaning is a huge part of it (<- insistence to talk about memnoch, see how armand puts it in tva with lestat trying to link up the things in his life rather than seeing them as disconnected).
on the other hand, show!lestat: gets pushed by gabriella to Be A Man and kill the wolves for that reason, gets asked by the band to join them and gets manipulated by gabriella to keep going with his music career (for her motives), gets a job at the theatre because of nicki, does not care about finding marius/leaving paris at all with gabriella seeming much more invested in it than he is, is left by gabriella rather than any kind of mutual falling out or leaving, HAS NO GREAT WISH TO TELL HIS OWN STORY AND MUST GIVE IT IN THE BAREST BONES (apparently why the flashbacks are so brief, right? lestat doesn't want to face his own past, right???) or COUCHED IN SONGS WHERE MEANING MUST BE INFERRED or REVEALED IN INTERVIEWS WHERE NARRATIVE MUST BE BULLIED OUT (unsuccessfully) BY BURNT-OUT JOURNALISTS to actually get the thing across kicking and screaming. he wants to be heard but seems to be making no earnest attempt to tell it until much later (3x05 with the album) in the story and then too under gabriella's influence (unlike book!lestat, who bares himself and his vulnerabilities in what i can only call a very moving performance (ofc he's not being 100% honest but he is Mostly earnest and sincere) of openness, without being asked to do it and at times (qotd night island bit with marius. among others) when being told to STOP doing it).
for book!lestat, agency is something quite important, something he strives towards, because it allows him to believe in himself as more than a nothing entity with no impact and an end of life which is going to mean nothing. (khayman gave a really great summary of this in qotd '88 actually. it's quite funny.) it allows him to be SOMETHING by virtue of DOING things rather than having things happen to him (even when in actuality the things did Happen and were not in his control). he takes charge of how his story is told but also does want to tell it because if he accepts it, he did it, and he is an active player in his existence. show!lestat instead seems to be stripping himself of agency in his own narration not just in situations where he did not actually have it (magnus, akasha blood drinking) but also in situations where he either did or should have (speech about 1x05 in the end of 3x05....if true then his being possessed would be narratively weak and optics wise AWFUL). he doesn't want to tell his story very fully at all because that means none of it happened and he is unhurt. (both are responses to trauma and pain but are different, close to diametrically opposite.) not to mention the plot changes. and ultimately this divergence i think becomes so profound that the two versions don't really end up feeling like the same character at all.
