I haven't played Dragon's Dogma, bit I can tell you: Sleeping Dogs is a hoot and a half. I really didn't expect much from it and only picked it up after reading over and over how good it supposedly is, and I'm realldy having the time of my life. Short breakdown:
The story/voice acting feels solid, but cliche-laden - in a good way. It's like bring in "one of these movies", but the presentation is great.
Leveling is done by collecting three kinds of XP, mainly tied to three different kinds of missions - two of which are mandatory. Additional combat maneuvers and health bonuses are unlocked via collectibles.
Driving is a lot of fun, even though I'm usually not into driving games. Once you got the hang of it, you can have lots and lots of giggles with stolen cars, including, but not limited to a couple of street races.
Hand-to-hand combat is intuitive and easy to handle once you've learned what to expect from which kind of enemies. It doesn't fell as fluid as in the Arkham games, but it's very playable. And the reaction of a handfull of thugs when you kick their friends' asses in front of them is priceless.
Freerunning isn't as over the top as in Assassin't Creed or Prince Of Persia, but it's a neat way to get around. I'd have wished for more rooftop action or something, but the occasional running away from cops or after a pickpocket is still good.
Gunplay feels a little clunky, but probably a lot more realistic than in other games. I'm just starting to get the hang of it, but it's the smaller part of the action anyway.
There are collectibles and a way for each kind to be displayed on your map. If you want to go for 100 % it's absolutely doable and a great way to get around in the city a bit.
The minigames are short enough to not become annoying and very few of them are actually mandatory.
Currency is used to buy additional apparel for XP-/Damage-/Shopping bonuses and new vehicles (cars and bikes). There's 5 different kinds of sets with 2 or 3 tiers each, all of which come in about 2 or 3 visual styles (read: color palettes).
It's fun, so this one you should definately get. So it's either Sleeping Dogs or both.