I've had both drugs a number of times, and seen both used in my work setting. For me they are relatively equivalent in action, though Versed takes a short several seconds longer to take effect.
Versed induction: I get a burning in my IV, not severe, but certainly felt as it courses up my arm. As it hits my chest the burn disappears, as the volume of the Superior Vena Cava dilutes the drug. Acouple heart beats and I get a "whOOSH!!!" sensation, increasing in strength, as the Versed hits my brain. I feel like I'm passing through a membrane of sorts, and then everything is just GONE! Later I waken suddenly and all is over.
Propofol (or as I like to call it, Milk of Amnesia) just goes from the syringe into the IV tubing, then NOTHING!!! I'm suddenly disconnected from the world, and then I wake up. No hangover, no nausea, just gone and back again. It works great.
I've worked on patients using both drugs for dislocations and fracture realignment. Both seem to work equally well, and each actually has a bit of a twilight period as patients come back around. I actually don't have a preference for myself, and it seems anesthetists tend to use one over the other by personal professional preference.
One interesting aspect of Versed in lower doses as a pre-op sedative, to reduce anxiety, is that a patient can appear awake, talking, interacting with staff and family, but not remembering the chat. And the patient sometimes seems to be a bit behind in processing things said to them and in their replies. That can be very funny, and patients don't usually remember it, or remember it very poorly.
I've also had my diaper changed several times but have no memory of being changed. I'd go to sleep in one of my premium diapers, and waken in a cheap hospital diaper. I usually like diaper changes, but don't remember any of those.
Just my $0.02 from the viewpoint of a patient and a medical professional.
Binkey