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In general you it's highly advisable to enter and leave a country on the same passport. Switching passports can be a bit of a chore depending on the actual entry and exit procedures and how much information the airlines (if you are flying) need to collect and transmit to the authorities.
I recently flew on a multi-country trip and switched passports on the leg from Germany to South Korea, i.e. I left Germany on one passport and entered South Korea on a different one. Lufthansa actually needed to know about this and collected the information accordingly. However, they were apparently used to doing this, so in this case, it was no problem.