I see two significant benefits to the internal hub 1) Ease of use 2) Low maintenance
If you're someone who could benefit from gearing, but are completely confused by deraileurs, this is pretty foolproof. Experienced cyclists may take it for granted, but I know several relatively intelligent people that just don't get it, let alone cross-chaining.
I sought out the Nexus8 for the low maintenance. Riding every day, rain or shine, an exposed drivetrain requires a lot of cleaning to keep it in proper working order. An internal hub keeps all the important bits protected in a bath of lubricant. The drum brake is a plus for me, as well, since it works in icy conditions when the front may not.
I have my concerns about removing the rear wheel efficiently (especially in the cold), and plan to practice a bit before I promote this bike to a full-time commuter this winter. If I can patch, I will likely just break the bead on one side and pull the tube out with the wheel still mounted, which I've done before. It may not be as easy as having the wheel removed, but I'm guessing its easier than removing THIS wheel. Puncture resistant tires and/or tire liners are good protection against this situation.
Ease of use and low maintenance come at a cost, and I see two: 1) weight 2) inefficiency
The hub has significant weight, which is concentrated in one spot. As someone who carries loaded panniers every day, this is negligible, and shouldn't deter someone from buying one. If it does, you're probably looking at the wrong bike to begin with.
I notice a bit of drag in the hub when I'm pedaling compared to a deraileur drivetrain, but only in some gears. I don't recall which ones, I think 3 and 7, but I hear a lot of gear winding sounds and notice the drag compared to the next gear up or down. I've already developed a tendancy to skip those gears. I'll try changing the oil and adjusting before blaming the hub, but I am picturing the planetary and sun gears spinning, which has to produce some resistance over a chainwheel and cog.