Similarities: both are chemical messengers, both can have (but don't necessarily have) similar structures (made from amino acids), both can be produced by the central nervous system (hypothalamus produces some hormones), certain molecules can act as both hormones and neurotransmitters (example: norepinephrine).
Differences: neurotransmitters are released by neurons across a synaptic gap, have very short distances to travel, and act very quickly on the neighboring cell. Hormones are released by glands and often have to travel longer distances, which means that they are slower-acting. Also, hormones are typically used for regulation (negative feedback) while neurotransmitters are used for stimulation of a neighboring cell.
