From what I remember from the animated series, Mister Sinister was creepy crazy, in that he liked experimentation and was obsessed with Cyclops and Jean and their future child. He would capture X-Men, connect them to machines and cackle. Apocalypse was all about human genocide and mutants ruling the earth with him as a king or god. I also remember Magneto as wanting dominance over humans, though he seemed to prefer allowing them to live on as slaves of the superior mutant species, rather than genocide. When I was looking at the Marvel site, they mentioned that Magneto performed genetic experiments as well, so it seems he's a hybrid of Apocalypse and Mister Sinister.
I watched the series as a kid, but I did some research to refresh my memory. Below is a summary what I found on the Marvel website. It's surprisingly not very detailed, considering Marvel is the company that made and owns these characters...
Mr. Sinister
His real name is Nathaniel Essex, and he became Mister Sinister through Apocalypse. Sinister is a mad scientist type, who performs experiments, has a desire to live forever, and is obsessed with Cyclops. He was so obsessed with Cyclops that he "created" Cyclops's son, Nathan, to kill Apocalypse. Nathan became Cable, a time traveling mutant. What's interesting about this, is Marvel's website lists Apocalypse as an alias for Mister Sinister.
Apocalypse
The first mutant, Apocalypse's real name is En Sabah Nur. He wants mutants to rise up as their own race and eradicate all humans. His history is filled with him enslaving four mutants as horseman, trying to kill all humans, being attacked by good mutants and dying or almost dying, only to reappear again later.