Solid-fuel versus liquid-fuel rockets.

Both solid-fuel and liquid-fuel rocket types have advantages and disadvantages. They are listed in the table below

Solid-fuel advantages Solid-fuel disadvantages Liquid-fuel advantages Liquid-fuel disadvantages
Very stable, durable Can't be turned off- once the burn starts, it goes until fuel is used up. Variable thrust- the amount of fuel and rate of burn can be changed in flight Fragile, many complex parts
More thrust for a similar size rocket Fuel decomposes, must be replaced. Liquid-fuel boosters are more easily re-usable Oxidiser (liquid oxygen) must be kept extremely cold.

(source 1, source 2)

As you can see from the table, the advantages and disadvantages for each correspond well, meaning that for some purposes sold-fuel rockets are very advantageous, and for others liquid-fuel rockets are more cost-effective. The best example of this is the space shuttle. The space shuttle uses both types. The boosters are made of an aluminum and perchlorate fuel, which burns very well and helps propel the shuttle into orbit. The main engines are powered by hydrazine and liquid oxygen, which gives much better control over the movement of the shuttle in space.

The space shuttle at takeoff. (source: 7)