"Spoiled" is usually used only in regard to children. The emphasis is less on giving the child luxuries, more on failure to discipline the child. There is an echo of the familiar proverb, "spare the rod and spoil the child" (if you never punish your child by beating him with a rod, you are not doing your parental duty).
The idea is expressed in "Tom Sawyer." (Aunt Polly is speaking in the colloquial English of Missouri in the 1800s; "spile" means "spoil," the "Good Book" is the Bible--although the Bible doesn't actually use that language).
" I ain’t doing my duty by that boy, and that’s the Lord’s truth, goodness knows. Spare the rod and spile the child, as the Good Book says. I’m a laying up sin and suffering for us both, I know. He’s full of the Old Scratch, but laws-a-me! he’s my own dead sister’s boy, poor thing, and I ain’t got the heart to lash him, somehow."
"Pampered" can be applied to children, to pets, or to adults. The emphasis is on luxury, excessive or unnecessary luxury. It's too much, but it's not actually wrong.
"She pampered her cat, feeding it homemade cat food with expensive fresh shrimp in it, instead of canned cat food."
"Pamper yourself at our resort! This week only, our deluxe suite, with Jacuzzi, balcony overlooking Niagara Falls, 82" TV, and complimentary champagne welcome basket, is just $1,295."
"He was a pampered child. His overprotective mother had him educated at home by tutors and he never experienced the rough-and-tumble of playing with other boys."