Crazy Kong is Donkey Kong's long lost European cousin. Some of these machines were actually licensed versions by Falcon, while others were bootlegs by Jeutel and other manufacturers. It appears that almost all Crazy Kongs that made it to America were the bootleg version, with some of them being labeled as "Krazy Kong".
The main difference between Crazy Kong and Donkey Kong is the sound, and color capabilities. Crazy Kong ran on hardware that had the same processor as Donkey Kong, but its video capabilities were lacking, and it had a totally different sound chip. Basically what all this means is that Crazy Kong had terrible sound, and some definite strangeness in the color area. The background music is missing entirely, and most of the sound effects have been changed. For example, in Crazy Kong, Mario makes a "Hiya!" sound when he jumps, instead of the "Boing!" that he makes in Donkey Kong. The graphics use slightly different colors, which change from level to level. The Kong animations are also different, and often do not match up with the in game action.
There are also mild changes in gameplay. Kong doesn't toss out nearly as many barrels, and there are other mild changes such as gaps in platforms that were not in the original, and the manner in which the elevators work has changed as well.
I personally have found that Crazy Kong is a lot easier than Donkey Kong, but the sound is so terrible, that I would rather just play the original. The game has a bug that effectively ends all games at level 22, so really good players may also find themselves limited there.
There were lots of different Crazy Kong cabinets. The most common one was similar in design to the Donkey Kong cabinet, but the artwork was more realistic, and ther monitor bezel had a circular clear area, as opposed to the rectangle that most games had. Crazy Kong could also be found in cocktail format. These were usually conversions, and were only decorated with an instruction card.
Where to play?
Personally I just recommend playing the original Donkey Kong. But if you want to play Crazy Kong, then you can use the MAME emulator, or wander the streets aimlessly for years until you bump into a real Crazy Kong machine.
This title seems to sell for much cheaper than the original. So you might find a good deal on a Crazy Kong machine. These machines can be upgraded with a real Donkey Kong circuit board for around $100-$150, and you can probably resell your old Crazy Kong circuit board to partially finance that.