I think a soul is your personal ability to make decisions as well as a being aware of those decisions ramifications.
Yet, a soul also is a thing that defies logic,thinking, and the sum of your past experiences; it is part emotion too. It allows us to either forgive or hold a grudge, love or hate, be loyal or traitorous, have empathy or not give a damn. It is part intelligence and part emotion, a bit of self awareness with a pinch of irrationality.(For me at least)
I also think its eternal, but that does not really play a part in this discussion.
I think vampires have soul as well, but when Giles or Buffy say they do not earlier in the season it is because the intelligence side of it is so foreign and the emotional aspect of it is so undesirable/evil/taboo that it does not register to them that as recognizable by what they would call a soul. That said, I don't think all vampires are the same when it comes to their soul/personality. I'm sure they differ just like us.
Remember that one vampire that Buffy first thought was the anointed one, the religious zealot? When he rose as a vamp he gave me the heavens warrior vibe- though very confused, the poor vamp didn't even know why a crucifix hurt it! This stuck in my mind and helped form what I think about buffyverse vamps. Who the human was prior to the formation of the hybrid plays a very big part, imho, at least as long as the human soul was well defined and the hybrid is not left with a blank slate as far as memories go. (in fact maybe that is why the master chose a child for the real anointed one, less world experience, fresh cookie dough that has not been shaped by all that much yet. It would allow the demon side of the hybrid a more undiluted/noninfluenced personality.)
When the vampire moves into the host and expels it soul there is still memory of the host left, which helped define that prior soul. I believe it also helps define the hybrid, and the strength of the influence depends upon the strength of the personality/soul of the victim as well as what kind of personality/soul inhabits it.
In the case of Harmony you get a harmonious exchange and she isn't really all that different than pre turned Harmony.
With the Spike hybrid you have a passionate but shy William and a passionate and boisterous Spike. William loves art and beauty...in short he just loves, love. Spike loves to fight and win/kill, feeding isn't even all that important...like the slayer in 79 when he broke her neck on the subway. Both know what it means to have a passion for something
When the chip was introduced to the hybrid it denied Spike his passion for hunting and fighting and he had to look toward other outlets, mainly Buffy. I believe he turned toward love because ultimately that is what William so craved and appreciated and it left it's mark on Spike.
With Angelus...well he seems an exception. You have two very different sides, and this Lliam fellow who I don't know jack about...is that Angel' mortal name? As was posted before you have three personalities forged by a shared experience, all very different from one another.
I'm not saying this is canon or anything, it's just my opinion on it.