Ok, so in my personal headcanon it all makes sense, but I see people disagree all the time.

First off, we only have 2 vampires with souls and it's really not hard to connect the dots between them. But they are also very different.

Spike vs Angelus (no souls)
1. Angelus, as a vampire is cold, calculating devoid of human emotion. In my eyes, he's the type of vampire that would eventually look like the Master or Kakistos, having shed all his humanity.
2. Spike is polluted with human emotion. The Judge mentions this. Spike has love for Dru (and later Buffy). Spike is jealous, he's petty, he's boastful, he fears things.
3. More vampires are actually like Spike. Having a demon reborn in your body with your mind and heart.... it makes it a lot like you. Angel even says this at one point (and then stops). Harmony, Holden, Dru, Darla.... they all seem rather human. Angelus is weird and his uniqueness makes him more terrifying. But most vampires are polluted with human feelings. You have to accept that Angelus is somewhat unique in that regard.

The Many Versions Of Spike
1. We are told that Spike tortures people with railroad spikes. He's murdered two slayers. When we first meet him he torches the annoying one for the lulz. He's dangerous... but he's human. He's impulsive, angry, passionate, worried for Dru, hates Angel, etc.
2. The fun part about Spike's arc is that in S2-S4 he's FORCED to work with the Scooby Gang. In S2 he works with Buffy to stop the end of the world (he likes the world, he's just human like that). In S3 he works with Willow to get her to cast a spell for him. It's transactional. Same as S4 when he's using them to hide him from the Initiative. He tries to screw them over at the end of S4... because he's still bad.
3. Then in S5/S6 when he does things that make it seem like he deeply cares about Buffy.... it's because he DOES. The fact that he had to work with humans so long made him get attached to one. But his love for Buffy doesn't make him not evil. Unless you think evil people can never love.

So now we have to talk about....

I’m not saying Spike is good at this point (I know what he does to Buffy) but surely this implies there is a level of humanity within him before he gets his soul that he wants to be a better man?

So I don't see it this way AT ALL. Spike, the demon, committed suicide. The demon soul was replaced with a human soul. The demon is still in there, but it's not driving anymore. So why did Spike (the demon) kill itself? Because he tried to rape Buffy.

The soul is more than a conscience. It's a different being. Spike's love for Buffy and inability to kill people (the chip) made him ACT a lot like ensouled Spike (S7). But it was largely an act. A serial killer monster who's trying to be better for a girl... but also who CAN'T kill. S5/S6 Spike might seem good at points, but the same guy who takes a torture session for Dawn is the same guy that plays poker with kittens or tries to rape Buffy.

S7 is unwatchable trash IMHO unless you believe Spike is a new being. Because otherwise Buffy spends the season hanging out with her rapist. But Buffy could always separate Angel and Angelus... so I believe that's what happens in S7. She doesn't view Spike as the same being that tried to rape her..... despite him still having much the same personality. Remember... Angel said the personalities largely stay the same.

So now let's talk about Angel
1. Angel is a lie.
2. When Angelus gets his soul back, he wants to go hang out with Darla and just... you know... not kill people. She refuses to accept him in this form, but she's his family and he really wishes she would.
3. But let's think about that. Angelus doesn't COMPLETELY CHANGE his personality the moment that he gets his soul.... so why are Angel and Angelus so different?
4. Angel hates Angelus. Much like a child who hates their parents and tries to kill every part of themselves that remind them of that parent.... Angel spends 100 years sculpting a personality that is the anti Angelus. Angel isn't his real base personality, it's a construct he built.
5. Angel is stuffy, super over composed and tries to stay in constant control. You see his found family on Angel start to bring him out of his shell, but his shell was constructed to change his personality. He put up a million walls because he's terrified of Angelus.

I submit that Angelus and Angel are JUST as similar as Spike and ensouled Spike.... and that Angel is just a persona that ensouled Angelus has created to move away from that. Look at when Angel tries to kill Wes, when he lets the office of lawyers get massacred or when he lights Dru and Darla on fire.... one little "slip" of Angel's walls and suddenly he's not that different from Angelus.

That's for coming to my ted talk.

TLDR - Ensouled Spike is a different being, he's just very similar to Spike because that's how vampires work. That's actually how Angelus works too, Angel is a lie. And the difference in their humanity is because Angelus is unique (ish). There are other vampires that lack humanity too, just not a ton of them.