For me a decent grade Heroin high is a lot better than morphine, not just more potent but different and more likable whether you snort it or IV it. After the rush it gives me a good feeling all over my body that I can't even describe, it also changes my personality positively, usually kind of shy or self-conscious but when I'm high really outgoing and not afraid to speak my mind or do things that I wouldn't normally do. It also makes me more active, I cannot just sit idle while high, I got to find something to do. I've experienced some of these effects on other opiates but to a much lesser extent. Alcohol gets me a kind of similar high but it impairs me and you crash after a while (plus the hangover).
The sex is also great on heroin I can go all night non stop, I admit that a couple times I've done too much heroin after being clean for a while and couldn't get it up even after a half an hour BJ but that only happened twice in over 20 years of use.
I've also tried IVing hydromorphone (Dilaudid) and it gives me a weird rush that I don't even like, in fact I hate it (and I love the heroin rush), the only time I done it again is if I'm very sick and I make sure to shoot it very slowly to avoid the rush.
As for physical dependance, heroin creates physical dependance much more quickly than other opiates (3 days) and the tolorance grows really quick, I can do a bag today after being clean for months and after a couple weeks I'll easily be doing a gram a day to get the same highl, also the withdrawals hit you real hard but they last a lot less than other opiates (the worse is over by the 3rd day), other opiates have milder withdrawals but they last much longer, personally I'd rather kick a heroin habit than any other opiate. Specially methadone which last for weeks, I tried to kick it many times and the only way I could do it was by going back into heroin for a month and then kicking the heroin habit and you need a lot of heroin when you switch from methadone but it's still much easier to kick once you've gotten the methadone out of your system. That's the one opiate I will never do again, its not only hard to kick but it totally messes you up if you take it long enough, it makes you very sensitive to sunlight, messes up your teeth and bones, makes you sweat a lot, and can ruin your sex life (it makes you come in less that 5 minutes although most times I could keep going but it's not the same and can be embarrasing). It also diminishes your desire to have sex and other things that are normally fun, I guess by the same mechanism that dimishes your desire to get high.
As for psycological dependance heroin is the worse for me, in fact is the only opiate that causes psycological addiction for me, I guess because it's the only one that gives me such a pleasant high, other opiates I only take for pain or for withdrawals so there's no psycological aspect to it, but for getting high heroin is the way to go. I can't count how many times I've kicked the heroin habit but after being clean for months if I try it one day I'm going to be craving it like crazy the next day and I usually fall for it so it only takes 1 time to get hooked up again. I know that and yet I been repeating that cycle for 20 years, everytime I do it I try to tell myself that it'll be just once but deep down I know it won't but I still do it, I don't really understand it myself!
For those of you who wrote that are considering to try heroin my advice is DON'T DO IT, you may fall in love with it and it will hunt you for the rest of your life, if I could change something in my life I would go back to the day I first tried it and don't do it. I'm not saying that it has totally destroyed my life, I'm a software engineer and live a decent life, but if I hadn't gotten into this habit I would've done a lot better, specially economically.
To answer the main question morphine may be almost as potent an analgesic as heroin but the high that you get from heroin doesn't compare.
I think those who favour morphine is because they haven't tried a decent grade heroin (which is hard to get in the US), also a lot of the heroin on the street is mostly morphine and monoacetylmorphine just because they don't "cook" (acetylize) long enough for it all to turn into heroin, most clandestine labs just guess how long it takes based on experience or heresay but don't really have a way to test when it's done.
As for the pharmaceutical grade diamorphine, if it came in liquid ampoules it hydrolizes completely into morphine after about a year, so they probably where doing morphine, also they're diluted in a solution that's about 1% heroin so it doesn't hit your brain in high concentration and hence no good rush, I once tried one that came as tablets on the ampoule and you need to add water right before shooting it, it was one of the best highs I've got, the rush wasn't that good but that's because you need to add a lot of water to disolve the tablet so you end up with a 1% solution again and that's done on purpose, they make is as an analgesic (or to treat whatever ailments), not to give you a rush. The same happens with high grade street heroin if you put too much water, the best way to get a rush is by adding just enough water to disolve the heroin and when you shoot it pull back just enough blood to know that you got the vein, then push the plunger as fast as you can, if you need a tourniquete to get the vein take it off before pushing the plunger. Also depending on which vein you shoot it it may have to travel accross your whole body before hitting the brain (getting diluted with blood along the way) so that also affects the rush, for me the best place to shoot is the big vein under the wrist to the thumb side, I believe that's the same vein that runs through the back of your elbow but I don't like shooting there ppl see some scar or track in there and they automatically assume you're shooting something, on the wrist is less obvious and you can cover it with a watch.
As for safety, I think if they were both regulated morphine would be safer, just because heroin hit's you faster so there's a greater risk of overdosing.