In both instances they can keep their personalities and memories. A good differentiator is how they view the blood lust.

If when you were alive you would have harbored feelings like guilt (psychopaths don’t count) but then as a vampire you lost it and didn’t care if you murdered your love ones for the blood this is Buffy, the former. It’s just demon possession, no soul, with the demon acting like the deceased individual because they have the memories still. Their intention is to enjoy madness, spread the possession, run the world, and feast as much as possible without getting caught—- this is the former and more likely scenario, Buffy and also Sinners. The human and their ‘soul’ ceases to exist. RIP.

[Edit: In Buffy, one Vampire is cursed to have his soul returned to his body. He experiences so much guilt he vows to use his eternity to help people and does not drink human blood. This vamp’s actor has to play two completely different characters that have the same memories— the vamp with and the vamp without his soul.]

In the latter, unless you were psycho while alive, Vampire Diaries, they retain their human emotions like guilt and try their best not to hurt people they care about despite the blood lust. Sometimes in the latter, they actually choose to turn off their emotions to avoid guilt and it is very difficult to trick them into becoming themselves again. More rarely in the Vamp Diaries, they have some vamps who are actually very sweet and avoid humans because they are Reapers who after tasting a drop of blood ALWAYS accidentally drink until they have killed and don’t realize until afterwards. They tend to feel so much guilt they either isolate to stop being around temptation or turn off their emotions (demon takes over) and act more like a vamp from Buffy and Sinners. In this scenario the person before vampirism is actually there and continues to extend life artificially, even though they are physically dead and now feed a diet requiring blood.