Usually a spinoff from another series doesn't run for as many seasons as the show it was spun off from. But then there are always exceptions. I know there are some but probably not that many. But let's see how many we can come up with.

For example Perfect Strangers ran for 8 seasons while its spinoff Family Matters ran for 9 seasons.

Ed.

Benson 7/Soap 4

The Jeffersons 11/All In The Family 9
The Simpsons 27 (and counting)/The Tracey Ullman Show 4

The Facts of Life (9) / Diff'rent Strokes (8)

The Game 9/Girlfriends 8

Barnaby Jones (8) / Cannon (5)
NCIS (15 +) / JAG (10)
Wanted: Dead or Alive (3) / Trackdown (2)

Extreme Makeover (4) launched:

Extreme Makeover: Home Edition (9)
Extreme Makeover: Weight Loss Edition (5)

Knots Landing: 14 years, Dallas(Original): 13 years

Some were better than the parent series. Facts of Life for example.