An electrical synapse is a physical connection between two neurons with a pore allowing charged particles (ions) to pass from one neuron to the other. Unless there are a large number of pores, or the pores are very large, the connection is weak, and doesn't cause an action potential in one neuron to result in an action potential in the other. Since electrical synapses can cause either neuron to influence the other, these are bidirectional synapses.
A chemical synapse is a junction between two neurons. The first (presynaptic) neuron releases a chemical (a neurotransmitter) which rapidly (in as little as 50 microseconds) crosses the small space across the synapse and binds to a receptor on the second (postsynaptic) neuron. This receptor may cause the direct or indirect opening of an ion-specific pore, allowing influx of sodium, calcium, or chloride or outflux of potassium ions. Since the presynaptic neuron can affect the postsynaptic neuron, these are unidirectional synapses.
Originally synapses were thought to be largely electrical, but it turned out that the vast majority are chemical. A large number of neurotransmitter and receptors exist in the brain (the main transmitters being glutamate and GABA). As for which are better, the chemical synapses allow a wide variety of responses, varying in duration and intensity (depending on the properties of the postsynaptic receptor, where the response can last from milliseconds to minutes or longer), so are almost certainly superior. Electrical synapses appear to be used to allow large networks of neurons to act in a more unified manner (for example, a single neuronal subtype in the cortex is wired to it's identical neighbors).
Source(s):
Kandel and Schwartz, Principles of Neural Science, 2000