They are free to play and offer similar cars and experience and both use the Unity 3D engine. So which one is better and which one should you get? I played both and here are my thoughts.
Kings of Parking starts by giving you a bus. It has two modes of camera, but both of them can make it hard to see where you are sometimes. The controls here are a tad easier because you have a "reverse gas" pedal instead of a gear stick. In most of the levels you have a couple of checkpoints to reach before you can park your vehicle. The game is lenient to scratches here and there and you should have no problems reaching your destination in one piece. After the bus you get to drive a limo and a sports car. There's also a bonus car - an Android truck. That one feels most like an arcade car and is quite fun to drive around.
In Total Parking, you start with a coupé, which is the smallest car here. Then you progress to limo, heavy truck and pickup truck. Total parking has similar controls to most other parking games - steering wheel, gas and break pedals and it has a stick with drive and reverse modes. The vehicles movement is a bit more realistic and the game is much less forgiving because each dent here means an automatic failure. The camera has more modes, but here the default camera works the best. It makes it somewhat easier, since you are almost watching the game in 2D.
ConclusionThe duel would most likely be tied. Both parking games offer a solid parking experience. Total Parking offers more realism and it is also more difficult. Players who like tough challenge would definitely like it. Kings of Parking 3D is an easier game and if your own car has been dented and scratched, you'd probably like this one better.
But in the end, both games are free and fun to play, so there is no reason why not get both and try for yourself!