That's a pretty comprehensive overview from Martin, so not much to add:
I have no experience with the 7-speed but was told by an executive of Royal Dutch Gazelle that it was good enough for commuter bikes (on the flat implied, basically what Martin says) and perfectly long-lasting if reasonably looked after. The takeaway was that the 7sp was cheaper for mass OEM fitment, but not rubbish. All the same, as a discriminating party (presumed; I speak Dutch with the same accent as the late Prince Bernhard) I was advised to buy the 8sp instead...
I have both the plain bearing and "premium" Nexus 8-speed boxes. In application there wasn't a lot of difference between these two boxes, thought the premium seemed a bit tighter, a bit snappier, but that may simply have been because it was on a prototype bike built by the boss and was maybe selected or even fettled. (I was once roundly abused by Jaguar for taking three E-types off the showroom floor and discovering on a straight piece of road that none of them would go over 138mph which, as I wrote scornfully, my ten year-old Maserati could also do. Apparently Jaguar would have preferred to lend me a specially tuned model...) I can't say whether the premium box is better than the plain one because I wiped both boxes before 5k miles.
However, I'm well aware that Shimano Nexus boxes with long, long miles of zero-service abuse on them run, and keep running, in The Netherlands and elsewhere, faithful commuters. Notwithstanding that I broke two, I admire those Nexus boxes: they're cheap to buy and well made and good value.
In use the Nexus box is smooth, easy-shifting; indeed, the computer-controlled Nexus electronic-shifted Nexus box on my Trek Smover changed gears imperceptibly. A Nexus box makes a Rohloff look agricultural (among other reasons because the Rohloff rose from agricultural roots, nothing to do with commuting or touring, everything to do with mud-racing), crude and rough. There is no reason to inflict a Rohloff box, especially a new Rohloff box, on people whose only cycling will be pootering around on the flat; the 307% range of the 8sp Nexus box is more than enough for them, and in fact, when I was fifteen years younger and a bit fitter, for me too. I can also see how the Nexus would be a fabulous commuter box, especially in flat places and places with lots of bad weather, where cleaning a derailleur system can soon get to be a chore.
As a touring bike, the Nexus doesn't quite have the range for big adventures away from canal paths. I wouldn't fancy going up the side of an Alp on a Nexus, unless I was 30 again and trying to prove something.
I can give you an example. On Nexus-equipped bikes, my fave rides were all on one side of town, and I'd climb about 250m per average ride; with the Rohloff, after two heart surgeries, my fave rides are in the hills on the other side of town, with between four and eight times as much climbing per average ride. (Sure, I have a motor, but most of the time it's off -- I use it near the tops of hills, and for the rest the Rohloff suffices well beyond where the Nexus would run out of gears.) Earlier today I was out walking with my wife, and we wandered across the precise short steep section where I first noticed that the Nexus was short enough of gears to kill me, and I should buy a Rohloff instead; it's only a few hundred paces from my front door; ditto, when I needed a motor, it was on that steep rise that I first realized it.
Also, I reckon that, since I wrecked two Nexus just with leg power, that you'd better not fit any but the limpest motors to a Nexus box; this is also the news out of the States but note that the nutters there fit motors three and four times as powerful as we do this side of the water, so it isn't surprising that they consider a Rohlofff de riguer. Since I prefer motors with a good deal of torque rather than outright power, that cuts the Nexus out for me, even if it weren't for the fact that those motors have history with me.
There are a lot of good reasons to buy a Rohloff if you can afford it, but not getting along with the Nexus -- within its perfectly respectable capabilities -- isn't one of them. One of the dangers of Rohloffing is that we get so used to the exceptional capabilities and longevity of the Rohloff that we can start to sound dismissive of other people's treasures; some of the people who ride with me consider the Nexus-equipped bike they have on order several steps up.
I agree with everything Martin says, even those subjects on which I have zero knowledge, like servicing the Nexus box. I was quoted 38stg plus carriage for the Nexus oil bath service kit, at a time when I could land a complete new wheel with a Nexus premium box in it for under a hundred quid, and a necessary tool was about the same, so perhaps it is just as well mine broke before I needed to make the decision, service or replace?
A final note: if you want a Nexus box, the smart thing is to wait until the winter. Over Christmas the European bike manufacturers, who buy Nexus Premiums by the ten thousands ready-built into wheels, sell off the wheels that weren't built into bikes, so there are all kinds of bargains on Germany Ebay (eBay.de). Some have "fitting kits" with them, but you can buy a fitting kit separately too, or get the parts from SJS or Petra or whoever your German supplier is; Shimano publishes brilliant technical literature from which you can get a list of components and how they fit together.