I had a huge response written last night, but my shaky internet connection died as it was trying to post, and going back doesn't remember the text.
Here it goes again, and I'll probably be a little more concise this time!
Have you ever owned/used a tablet PC? I ask because there are really two parts to answering the question of how easy it is to write on. The first will be the same for any stylus/tablet combination and the second is eDGe specific.
Firstly, the experience of using a stylus (plastic and smooth) on a tablet screen (glass or plastic and smooth) is inherently different from pen and paper. Some people adjust, some people will always find it a bit weird. It's smoother, with a lot less friction. To me, it's like the difference between using a full-sized, virtual keyboard and a physical keyboard: the motions are the same, but the tactile feedback is missing. If you go to any computer shop and try out a tablet PC, that will more or less be the "feel" of using the eDGe. I have owned several tablets and I would say it "feels" pretty much the same.
As for the eDGe in particular, the display does lag slightly behind your handwriting motion. The timing varies depending on the background you're using. I've found that if you use the blank (not lined, not graph etc.) background for the journal app, there's almost no lag. In this way, the experience is extremely similar to using Microsoft Journal for tablet PCs. (And, the eDGe's software is I believe a variation of the linux variation of that very same program - so the two programs are really similar, too.) If you choose lined or graph paper and are writing very quickly, then the writing can lag as much as a couple of seconds behind your action. The good thing, though, is that it captures everything. So, if you can write without the visual feedback, then no worries.
So in brief:
1. How fast? As fast as you want to go, but the display could very well lag behind you. It will capture every stroke you make, though. I do find that if I slow down from my normal speed just a tad, I get really, really, good results. If I go super fast, it's totally legible (but, I'm ok without the visual feedback to keep writing) and smooth enough, but I often do want to go back and tidy it up after in places. Not bad for school notes, since a lot of students rewrite notes anyway as a study technique.
2. How easy? Very. I love it. But, if you're writing a lot remember that the pen it comes with is more the size of a small (not standard size) pen. You may wish to consider one of the penabled alternatives suggested in another thread, though that's another purchase and they don't look particularly ergonomic. I am used to years of tablet PCs so I don't particularly struggle and am familiar with the technology currently out there and its limitations in use, so I think I probably have more realistic expectations than some others who might expect miracles.
3. Replace pen and paper? Tough and probably subjective call. For me, I would say yes. I used tablet PCs extensively for taking to meetings, tutoring students etc. and I did not need paper when I had a properly powered and working device. I have said in other threads that I am quite happy with how the journal app works on the eDGe and it's comparable to a tablet PC-lite experience. You do need to take into account battery life constraints and your usage/charging habits, of course to make sure you have power to use the thing. You also need to remember that all these journal notes you take go into one big library folder (unless you download an Android file organizer app) but can be organized by tabs, so you'd need to be OK with that kind of organization/retrieval system for these notes. Then you have the issue of backing up (I would probably export to pdf and send to my main computer) because you wouldn't want to lose your class notes.
Bottom line is, if the unit were working and I knew I'd have enough battery life or access to an outlet, I personally would have no reservations about using the eDGe as my class notebook. In fact, I would love having my notes in this form so I could "clean them up" on the page, then create pdfs.
I've mentioned elsewhere about my current inability to charge up (probably an adapter issue, but maybe the battery or the unit itself) which is why I can't do a video demo for you right now. But, maybe my thoughts re: the writing are helpful.