I have spent 25 years recreationally using lsd, psilocybin, and recently have dabbled with DMT. I can tell you that there is definitely a difference in all of them, which becomes more pronounced with larger doses.
With LSD I find that low or even microdosing is very socially liberating. I am naturally leaning on the extrovert side, but I've seen this with introverts in that it genuinely makes you interested and want to better know your surroundings, people around, and it lowers inhibition. It also provides quite an energy lift. The higher the doses, the more the social aspect begins to fade and it becomes more internally enlightening. I prefer to be with a couple/few others in like mind set and in nature or outdoors. I like that I can "control" the visual portion when on LSD and really, the physical piece as well as I generally have a lot of energy. The only thing I can't control is my smile. I can never stop smiling.
Shrooms tend to make me lazy and rubbery, with little motivation. They also tend to be very visual for me, which can be good or bad. Auditory senses are heightened, which makes them fun at shows/concerts. My biggest issue with them is that they are so unpredictable, so I always start low and work up, but then I've had times where they all hit me at once, basically leaving me incapacitated and unable to walk, which is the exact opposite of LSD.
DMT I've only tried about 5-6 times now and I cannot say I will do it again as I'm not sold on it. I've tried different doses and settings to see if it changed things and it didn't much. What I can say is that it hits you VERY fast, like in 5-10seconds, and then you lose all track of time. 1 minute feels like 15. There is zero motivation, it just makes me want to sit on a couch under a blanket and be left alone. It is not social at all, but it is very powerful. Basically, take a couple hits and it hits like a truck, you turn your head and the trails follow. So I sat staring straight ahead as to not get dizzy and then I got lost in my own thoughts. Going back to middle school, I thought of friends I hadn't thought of in 30 years and it was so vivid and real. I can definitely see that if you were working through some issues and had a guide, they could get some stuff figured out. Of all of them, I see the theraputic benefits the most with this.
Hope this helps a little.