Suicide Squad is a government mercenary group with a rotating membership, they are basically doing jobs for Waller and they get something in return (shorter sentences and suff).
Secret Six (the Simone version, there was a completely different SS in the 70's) are a band of supervillains, the group was formed before Infinite crisis in the Villains united title (that was basically the origin of the team) and as victorxd1999 said they are villains for hire and they have their own code of ethics (and when I say ethics I'm thinking about very loose morals).
I never read Suicide squad but the Taskforce X episode in JLU was awesome (which was basically a Suicide squad episode) and the new Assault on arkham animated feature was really entertaining (and bloody) too. They should rerelease the Ostrander run in chunky trades, I heard it is fenomenal.
On the other hand I've read all of Simone's Secret six and it is BRILLIANT! The whole team dynamic is just f@&ked up, Bane is hillarious and the Catman-Deadshot buddyvillain duo is my favourite team up of all time I think (Catman! Bloody Catman! and he is a badass!)
Oh, and King Shark of course: