Amenity and luxury both denote something (as an object, a feature, a quality, or an experience) that gives refined or exquisite pleasure or is exceedingly pleasing to the mind or senses.
Amenity typically implies a delightful mildness, gentleness, or softness, especially in contrast to an uncomfortable or distressing harshness, roughness, or crudeness.
- many English go to the Riviera in the winter because of the amenity of its climate
It may imply no more than a vague conducing to physical or material comfort or convenience.
- every amenity . . . including… showers, central heating, and first-class cuisine
—H. G. Smith
Luxury stresses keen, often voluptuous, enjoyment and unalloyed gratification of the mind or senses, usually without a special suggestion of opulence in the thing enjoyed or sensuality in the pleasure.
- and learn the luxury of doing good
—Goldsmith - Mark decided to walk back by the road . . . instead of indulging himself in the luxury of once more rejoicing in the solitude of the green lanes
—Mackenzie - a dressing room with a marble bath that made cleanliness a luxury instead of one of the sternest of the virtues
—Shaw