Liquid propelled Rocket engines work on various cycles such as pressure-fed, pump-fed(gas generator,staged combustion, expander, etc) and these have various design trade-offs between complexity, reliability, operational simplicity, development cost(?) etc. What are the various trade-offs between these cycles?
Disclaimer: I am not professional rocket scientist, information is primarily gathered through internet. This answer is provided with NO warranty.
This answer mainly focuses on liquid fuel engines.
Very simple design that does not have pumps. Can be easily started. Chamber pressure (and thus the specific impulse) is very limited compared to other cycles. Mainly used in upper stages as low chamber pressure makes operation in atmosphere difficult.
Simple design that uses cryogenic propellant to drive the pump (and cool the engine). Chamber pressure is similarly limited, also commonly used in upper stages.
More mechanically complex than the previously mentioned cycles, as it uses a pre-burner to drive the pump.
There are several advantages to the gas-generator cycle over its counterpart, the staged combustion cycle. The gas generator turbine does not need to deal with the counter pressure of injecting the exhaust into the combustion chamber. This simplifies plumbing and turbine design, and results in a less expensive and lighter engine. - Wikipedia
Chamber pressure is not as limited as in the previously mentioned cycles. It can be (and often is) used in first stage, as the low complexity makes developing larger engine easier.
Oxidizer-rich staged combustion
A more advanced design. staged combustion allows greater chamber pressure and higher specific impulse, at the cost of heavier and more complex engine. This cycle is usually used by LOX/Kerosene engines, as the counterpart - Fuel-rich staged combustion cannot be used in LOX/Kerosene engines, due to extreme coking problem. Oxidizer-rich environment proves to be extremely difficult to handle. Russia developed alloy materials to withstand the high-temperature and oxidizing environment.
Fuel-rich staged combustion
Similar to oxidizer-rich staged combustion, this cycle is mainly used by LOX/LH2 engines (and any other engine that does not have coking problem and wants high specific impulse). I guess the fuel-rich environment is easier to handle than the oxidizer-rich one.
Full-flow staged combustion
Extremely complex design that has the greatest specific impulse and mechanical complexity. The only built examples are RD-270 and Raptor.
Complexities of engine cycles are usually positively correlated to development costs. Reliability depends on the exact design and technology of the engine (e.g. redundancy)
- Encyclopedia Astronautica http://www.astronautix.com/
- The English Wikipedia
The question is somewhat vague, and so it is unclear whether you're asking about types/ categories of engines, or the actual cycle types. In general...
Solid fuel rocket engines
Pros: - Very simple and very reliable (no moving parts) - High thrust - Fuel is relatively safe for ground handling (often is just acrylic)
Cons: - Once they're lit... they're. No cutoff mechanism aside from burning through all the propellant - Because of that (^), can be relatively inaccurate in terms of trajectory - Typically non-reusable, but depends on housing material and characteristics - Low ISP - Large and heavy
Liquid/ Bi-propellant/ Tri-propellant Engines
Pros: - Moderate ISP - Moderate/ High thrust - Can be toggled on/ off - Because of (^) can be used repeatedly
Cons: - Much more complicated - Much less reliable (many, many moving parts) - Fuel (and overall system) is typically dangerous for personnel. Hydrazine a common liquid propellant is extremely toxic - Requires 2 forms of media -- an oxidizer and a propellant - Large and heavy
Pros: - Extremely high ISP - Designed for extremely long lifespans (and thus, highly reliable) - Much smaller form-factor/ weight compared to liquid and solid engines - Typically few to no moving parts - Over long periods of time, can eventually reach velocities much much greater than that of the other forms of propulsion
Cons: - Low thrust - Because of (^) cannot be used for launch -- only in-space maneuvering - Depending on the type, can be costly and complicated -- but this isn't always the case (such as with Phase Four's RF thruster)