My husband feels that Spike's soul is like (to paraphrase his very eloquent discourse on the subject) the ending of The Wizard of Oz where the scarecrow, tin man and lion all were told they already possessed what they sought. All they needed was the outer trappings. The scarecrow was given a diploma recognizing the wisdom/learning he already had. The tin man got a ticking watch to emulate the heart he already had and the lion a medal to honor his already existing courage. Jim says Spike was already well on his way to redemption and had the things everyone attributed to a soul in budding form. All he lacked was others recognizing and accepting he did have those traits. The soul forced others to recognize what was already there.
I think Jim might well be right. Having a soul in Jossverse didn't make anyone good, make one have empathy or compassion. It didn't make someone's choices easier or better. It didn't make anyone feel remorse either.
Having the soul might have caused Spike terrible guilt. Not sure why though because the soul wasn't present when the "crimes" were committed, why feel guilt over something you weren't there to abet? That would be like Buffy feeling guilt over Faiths acts when she hijacked her body. Then again that torture might ahve been the FE messing with Spike too.
The major difference I saw in Spike with a soul was it seemed to diminish his self confidence. Without the soul he was filled with a "never say die" attitude. For example his determination that sooner or later Buffy would love him or earlier his confidence that he could torture Dru into loving him again (IE doing what she desired, being what Dru wanted and that was the torture purpose). He would have argued with anyone who said his plight was hopeless.
After the soul he no longer felt worthy of her love. He agreed with her assessment of his character (evil, monster, etc.) and allowed Angel to further undermine his confidence when he returned after Chosen. He would NEVER have allowed that without the soul. He'd have told Angel to bugger off and would have hunted down Buffy hoping she'd let him close in some way and that eventually she'd care. With the soul he was much less sure.
Without the soul he "read" Buffy's actions. He saw that she was attracted and that she had feelings in spite of her verbal denials. It led him to try to make her admit the feelings in Seeing Red, a complete disaster! He was still reading "yes" and this time her "no" really was a no.
When he came back with the soul (after the madness) he SAW as we all did that she did care, that he mattered but he no longer believed what he saw. She said nothing so he "saw" nothing any longer. When she finally DID say the words he had (provided he meant the "no you don't") no confidence left to believe it. Soulless Spike would have gloried in finally having the proof of what he knew all along, "I knew it! I knew you did! Thank you for saying it."
Of course Spike might have believed her words and wanted her to leave, be safe (and didn't feel worthy for that matter).
The dint in his self worth, his confidence was the real difference. He lost some of his swagger but got it back by the time he was with Angel.
Another thing and I believe it reflects his sense of self worth for that matter is his surroundings. Without a soul he made a grave and hole in the ground downright homey! He was surrounded by lovely, rich rugs and books and a comfy bed. After the soul he was a guest first of Xander and then Buffy living day to day with nothing to personalize it and the circumstances had a lot to do with that. When he moved into the place in LA that Lindsey got for him he never added a thing until the video game and that was for physical therapy. Nothing of his personality was evident. It was as if part of him didn't feel deserving of beauty or comfort. His new life was all duty (and tormenting Angel)...work, taunt and sleep. Some of his joy in life seemed to be on hold.
He did not become more inclined to fight choices. He didn't develop immediate empathy (his too funny and honest rant at the woman he saved in the alley is a good example. Compassion was there, he saved her but he didn't suddenly understand that maybe she had no choice but to be in that place in heels or worry about her feelings as he rightly told her off). He wasn't any more "good" than he was before. He was no more self-sacrificing than before. He wasn't more diplomatic or anything else that wasn't already there without the soul. He had no greater wisdom. He didn't wallow in guilt like Angel either (and was that Angel's soul? He didn't have much moral insight as Liam after all. Was the guilt part of the curse?).
I think he did not need the soul for redemption. He was on the road to that already with each baby step, each choice.
Spike without a soul made choices based on pleasing the person(s) he love; Dru, Buffy. Let's face it most of us have a pay off for our good choices. Little is altruistic for any of us. Even if it is the good feeling we get about ourselves and the world when we do a good deed...there is a pay off. Some people do/choose good in hopes of an eternal reward (or fear of eternal punishment for otherwise). Some do it for our reputation (and isn't that to meet the requirements of others?). With the soul he MIGHT have been quicker to expand those whose opinion he cared about but he was doing that the more he was around people without the soul. First only Buffy, then Joyce and Dawn (because they mattered to Buffy first but in their own right in time), Tara and the others began to matter to varying degrees as he came to know them. The soul didn't change that.
However...and this is a big deal .... others, especially Buffy, would never have accepted his redemption as real, his ability to make right choices, avoid going back to his old ways without the soul. Their minds firmly demanded he have a soul to be credited with acceptance. For that reason he had to have the soul. They never seemed able to understand that souled people kill all the time and that the soul didn't guarantee that Spike wouldn't hunt and kill again. They didn't seem to see that he was already making good choices and that having a soul was no guarantee that someone would do so. It was so important to their perception of him and his worthiness that he really had to get a soul if he hoped to be fully let in, fully trusted.
Did he need the soul? Depends on what you mean by need. To be accepted, recognized, trusted by others? Yes, probably he did. To actually act and choose properly to deserve acceptance, recognition and trust? No, I don't think so.