Pro and cons of each vary. Lets start with the outdrive first...

Pros:
Efficient. Next to an inboard, the most efficient propulsion around.
Control. No other drive system give you better all speed control, even when
backing (Inboards have precise forward control, but virtually none in
reverse.

Cons:
Expensive. Most expensive propulsion system you can get.
Complex. The most moving parts of any drive system.
Water depth. Has the deepest draft.

Now the jet drive...

Pros:
Inexpensive. Cheapest drive system there is.
Un-complex. Only 2 moving parts on a standard drive.
Water depth. Can operate in the shallowest conditions. In some cases,
inches.

Cons:
In-efficient. Even the best jet is only 85% efficient to a prop boat.
Control. "Spongy" control (compared to an outdrive). Needs thrust to turn
effectively. Has limited, to NO steering when not under power.

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It's just about going fast...that's all...

http://home.insight.rr.com/cgreen/