I have a Specialized Turbo that I commute and run errands on.
The first time you ride it, you can’t help but giggle. The acceleration is effortless…
My opinion is that over all it is no faster than a road bike, but much more convenient / less effort.
Faster on the uphills, similar on the flats, slower on the downs. Differing abilities may have differing outcomes.
If I kit up and ride to work on my road bike it takes me the same amount of time as the E-bike, except on the E-bike I’m wearing a t-shirt, shorts and have my panniers full of lunch, work clothes etc.
Pulling my 2 kids in the chariot with their striders, lunch etc. to the bike park? Turbo, No question. Quick trip to get something from the store? Hop on the turbo. It’s actually as fast if not faster than driving over. One pannier has a lock, extra clothes etc etc. So I never need to remember that. Motor pacing a group ride? Not going to happen. Motor cuts off at 24mph and its hard work to go much faster.
When I commute and I’m looking for a bit more aerobic work, I turn the assist down to ~50% which I feel mimics the workload of riding a road bike. Remember, these things are heavy, have tires with crazy rolling resistance and are aerodynamic bricks.
With the assist turned off it is like riding in sand.
In terms of off-road e-bikes. I’ve never ridden one.
I don’t think they will tear up trails any more than a rider with strong legs does more than one with weak legs. You have to pedal smoothly. The higher the cadence the better. Standing is really awkward as the assist kicks in later in the pedal stroke (at least on my Turbo, maybe no Levo or other motors). Going up smooth climbs with steady pedaling, they will be faster. Going up technical climbs with a lot of bike handling they will be harderI’m not sure less-skilled riders will get over their head. The places where the assist helps, smooth climbs, skill isn’t a limiter. The places where it doesn’t, technical climbs, it will not help and may actually dissuade riders as the bike is heavy to push. On flat terrain speed is typically dictated by how fast you choose to go rather than your fitness level / ability to push the pedals.
Would I buy one an off-road Ebike? No.
I rode a handful of e-mtbs at Interbike Outdoor Demo last fall and I can fill you in on some of the off-road stuff.
On gravel roads, my first thought with the e-assist was “Dang…I need to react/bike-handle more like this is a motorcycle”.On rolling single track, they can be significantly faster for a given effort (depending on what power level you choose)…which can sometimes get you in trouble (on multiple levels) :-/On downhills, you REALLY notice the extra weight…they handle like pigs.
Now then, I also rode an e-Fat Bike (right after riding a Surly Ice Cream Trucker)…and I have to say I could see a purpose for them there. Fat Bikes are fairly heavy to begin with, and the e-assist basically made that feeling of “heft” go away on climbs and rolling trails. Didn’t seem to be as much of a difference for descents as I noticed for a regular MTB, but probably because the added weight is less of a percentage difference.
So…I came to the conclusion that their best application off-road is fat bikes…with the most perfect application probably being on a fat bike tandem 
Just my 2 centavos…