Sleeping Dogs, combat system aside, is like every other sandbox game you've ever played
Saints Row The Third, on the other hand, has you jump out of an airplane without a parachute, fight guys in mid-air, crash back through the airplane in a different direction, steal a parachute in midair and then land like a boss.
and that's just the scripted level
Fixed.
Saints Row the Third also has you shooting hundreds of brain dead AI bad guys, grind (albeit, amazing) character/gang upgrades for hours, driving around a city with very uninteresting road design and average driving controls, take part in some fantastic mission design (and a few clunkers that almost always involve being a copilot in a helicopter, for some reason), and experience a really dumb story that knows that it's really dumb and has fun with its own concept at every turn.
Sleeping Dogs has you fighting people in the best melee combat system in an open world driving friendly game, has some of the best driving controls that the genre has to offer, has some very fun roads to drive down, pretty mundane missions with decent presentation, a rapid paced character upgrade system with relatively tepid upgrade rewards, and a very predictable "serious" story.
Both games have their strengths, both have their weaknesses. Saints Row 3, I feel, is the better game but I have had more fun just driving around in Sleeping Dogs than I have had in many other games this year. Ultimately, the sheer insanity that is the second half of SR3's story just brings a smile to my face every time I think back on it.