Which engine type gives more HP- two or four cycle?

Theoretically, with all other factors being equal, the 2 stroke engine should produce 2 times the power of the 4 stroke engine. The reason being that the 2 stroke engine has twice as many power cycles as the 4 stroke per revolution of the engine.

Of course theory is one thing and it doesn't quite make it all the way to practice. Two stroke engines suffer from some inherent drawbacks that prevent them from achieving their full potential. The most significant of these is that they end up being less efficient due to several factors:

1. Incomplete combustion due to the exhaust ports opening up while the charge is still burning.
2. Incomplete "scavenging" of the exhaust gasses which then prevents a full fresh charge from filling the combustion chamber.
3. Lubricating oil in the air/fuel mix which hampers the combustion process.

For some specialized applications, however, where low weight and relatively high power output is needed have used 2-strokes almost exclusively until recently. For example outboard boat engines have historically been 2 stroke. Handheld outdoor power equipment (chainsaws, string trimmers, blowers, etc.) still often use 2 stroke designs. Also many model/radio-controlled aircraft use 2 stroke engines.