For the average person without preconceived preferences or sporting notions,

Extremely comfortable ergonomics.
Smooth, stable ride even over very rough surfaces.
Light, responsive handling without being nervous or twitchy.
Carry lots of weight without ill effect on handling.
Virtually maintenance free.
Durable.
No regularly consumable parts other than tires.


The down side,

Heavy.
Slower than a road bike.
Tire change or repair requiring wheel removal takes longer.
True Dutch/roadsters not common and expensive in NA.
Tire size not stocked in most LBS.

Most of the commonly parroted "limitations" pertaining to distance and hills are utter nonsense, if one chooses a bike with a 7 or 8 speed IGH which offers the same gear range as many contemporary bikes.
UPS delivered my Gazelle the last Friday in January, as of the second week in March I already have over 1300 miles on it, including several centurys, and daily commuting. And Western Washington is far from flat.

Also, being big tall bikes, ones ability to see and be seen in an urban environment is greatly enhanced. A coworker mentioned to me that he always recognizes me because he can see me several blocks away, compared to those on "racing bikes riding all hunched over" that cant be seen until practically on top of them.